Introduction to Mechanical Vibrations

Format: Hardcover

Language: English

Format: PDF / Kindle / ePub

Size: 8.99 MB

Downloadable formats: PDF

Credit: Timothy Yeo / CQT, National University of Singapore Here's a nice surprise: quantum physics is less complicated than we thought. It's because the Infinite field they're exploring is just that... But then all of that velocity will essentially go to zero because he's being tugged by the rope to the left. Also, the theory is currently limited to describing the simplest interactions between particles and electromagnetic fields. “It is not by itself capable of representing very much physics,” Oxford University physics philosopher David Wallace told Quanta earlier this year. “In my own view, this is the most severe problem for the theory, though, to be fair, it remains an active research area.” Nobody is claiming that quantum mechanics is wrong; there is too much experimental evidence that the equations do make accurate predictions about how things work at the subatomic scale.

Pages: 412

Publisher: John Wiley & Sons Inc; 2nd edition (May 1979)

ISBN: 0471820830

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We now address Newtonian mechanics in the case where the force on a particle is conservative Recent Mathematical Methods in Nonlinear Wave Propagation: Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo ... 23-31, 1994 (Lecture Notes in Mathematics) http://phpstack-9483-21148-60252.cloudwaysapps.com/library/recent-mathematical-methods-in-nonlinear-wave-propagation-lectures-given-at-the-1-st-session-of-the. The duo fired electrons at a crystallized nickel target to observe wave-like diffraction patterns. Till date, such a pattern was only observed for light waves. Thus it was conclusively proved that particles behave like waves and vice versa. In 1926, Erwin Schrödinger formulated an equation that described the behavior of these matter waves ref.: Grand Unified Theorem read epub http://vansco.net/library/grand-unified-theorem. Basically, with this Cat Question we are asking “When is the cat's fate decided, and how?” Quantum Nonsense in Mystical Physics — The cat's fate was delayed for two weeks because the quantum event – when electron hits wall – is not "completed" until the event-result is observed by the consciousness of a human. This proposal for consciousness-created reality differs from the.. The Wave: In Pursuit of the read epub http://blog.malvenko.net/?lib/the-wave-in-pursuit-of-the-rogues-freaks-and-giants-of-the-ocean. Splung.com is being continuously updated. At present, the site contains sections on mechanics, electricity and magnetism, optics, heat and thermodynamics, nuclear physics and cosmology with more sections in the pipeline. Google honors the physicist today with a Doodle. We explain the science behind his famous paradox. Erwin Schrödinger, one of the fathers of quantum mechanics, is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933 [ [ [ Waves in Oceanic and download epub download epub. But only certain wavelengths will `fit' into an orbit Hydrodynamics of High-Speed Marine Vehicles download pdf. Please note that this resource requires Java. Additional sources used for selected topics in the course: Time-independent perturbation theory Degeneracies and near-degeneracies; linear and quadratic Stark effect; Van der Waals interaction; fine structure, hyperfine structure and Zeeman effect for hydrogen Variational and minimum principles for bound states Time-dependent interactions Interaction picture; perturbation theory; "golden rule"; magnetic resonance; Born approximation; periodic potentials; energy shift and decay width; interaction with the classical radiation field; photoionization of hydrogen; photoabsorption and induced emission; oscillator strengths Symmetrization postulate Permutation operators; exchange degeneracy ( Messiah) Applications Scattering of identical particles; ground state and single-electron excitations of atomic helium; hydrogen molecule (Baym); central field approximation for many-electron atoms; spin-orbit interaction; angular momentum quantum numbers; Hund's rules (Bethe and Jackiw) Young Tableau Application to two- and three-electron systems; non-relativistic quark model; proton and neutron (flavor-spin) wave functions and magnetic moments Time-independent Formulation Lippmann-Schwinger equation; outgoing-, incoming- and standing-wave solutions; Born approximation and Born series; unitarity relations; optical theorem; distorted-wave formalism; eikonal method Method of partial waves Partial-wave expansions of wave functions and scattering amplitudes; phase shifts and unitarity; integral equation for radial wave functions; threshold behavior; Breit-Wigner resonances; effective-range expansion; variational method; scattering by a hard sphere Jost functions Analyticity (Goldberger and Watson); enhancement factor; S-matrix poles and zeros (Schiff) Electron-atom scattering in Born approximation Transition form factor; large and small momentum-transfer limits; inelastic scattering (Bethe and Jackiw) Coulomb scattering Rutherford cross-section; partial-waves; inclusion of short-range potential (Messiah) Spin-dependent scattering Partial-wave expansion; spin-orbit interaction; pure and mixed spin states; density matrix Time-dependent scattering Propagator theory; time-evolution and scattering operator; Lippmann-Schwinger equation (Schiff) Photon picture; spontaneous emission deduced from correspondence principle and semi-classical theory (Baym); angular momentum and photon spin (Messiah); dipole approximation; selection rules and polarization properties; Thomson scattering; Raman scattering; Bethe's treatment of the Lamb shift (Baym) Solutions Dirac matrices; plane-wave solutions; helicity states; inclusion of external em field; Pauli equation and relativistic corrections; spin-orbit and Darwin terms (Baym); separation of angular and radial dependence; hydrogen atom (Schiff) Lorentz covariance Conserved current; Lorentz transformations and space and time reflections; proof of covariance; angular momentum as generator of rotations; charge conjugation; scalars, vectors, and tensors; plane-wave solutions; projection operators for states of positive and negative energy and helicity (Bjorken and Drell)

Inspired by Debye's remark, Schrödinger decided to find a proper 3-dimensional wave equation for the electron. Hamilton 's analogy between mechanics and optics, encoded in the observation that the zero-wavelength limit of optics resembles a mechanical system—the trajectories of light rays become sharp tracks that obey Fermat's principle, an analog of the principle of least action. [12] A modern version of his reasoning is reproduced below , e.g. Perspectives of Strong Coupling Guage Theories Perspectives of Strong Coupling Guage. You will find YouTube videos by me (I have also published a dozen scholarly articles in professional journals of physics and mathematics). Waves are everywhere in nature - and I mean everywhere. The surprising/astonishing/amazing thing is; all types of waves are almost identical in behaviour , e.g. Essays on the Formal Aspects of Electrom read here. Recently he has succeeded in an especially daring design through his ingenious idea for the solution of the former particle mechanics by means of wave mechanics in the differential equation he has set up for the wave function…. Schrodinger himself has already been able to deduce many consequences from this fortunate discovery, and the new ideas that he has inspired with it in many fields are even more numerous…it may be added that in lecturing as in discussions Schrodinger has a superb style, marked by simplicity and precision, the impressiveness of which is further emphasized by the temperament of a South German.” Sommerfeld was the first choice and when he declined to leave Munich the offer went to Schrodinger ref.: Applications of Noncovariant download online download online.

Wave Mechanics of Crystalline Solids

If the universe is infinite, and there is infinitely more matter beyond the visible universe, that gravity would be balanced, and there would be no reason to postulate a cosmological constant at all , source: Mathematical Theory of Hygens' Principle. Mathematical Theory of Hygens'. Hindus believe the world observed through our senses is an illusion, and the actual reality (the universe) is itself God , e.g. PARTON ET AL:APPL ELECTROMAG, download here http://warholprints.com/library/parton-et-al-appl-electromag-netics-2-nd-ed. Each vibrates at the same frequency - the frequency of the wave. The waves all travel at the same speed in a vacuum - 2.998x108 ms-1. They are unaffected by electric and magnetic fields, and in general travel in straight lines. They are transverse, and therefore can be polarised. They can be diffracted, and can interfere with one another Renormalization and Invariance in Quantum Field Theory (Nato Science Series B:) http://warholprints.com/library/renormalization-and-invariance-in-quantum-field-theory-nato-science-series-b. Damping is the decrease in the amplitude of an oscillating system. An oscillating system experiences damping when its energy is losing to the surrounding as heat energy Vibrations and Waves in Physics warholprints.com. Paradoxical principles including the classical limit, the uncertainty principle, and the complementarity principle were made necessary Surface Waves and Fluxes: Volume II _ Remote Sensing (Environmental Fluid Mechanics) (Volume 2) http://warholprints.com/library/surface-waves-and-fluxes-volume-ii-remote-sensing-environmental-fluid-mechanics-volume-2. The time-dependent Schrodinger equation allows us to calculate the wavefunctions of particles, given the potential in which they move. Importantly, all the solutions of this equation will vary over time in some kind of wave-like manner, but only certain solutions will vary in a predictable pure sinusoidal manner , e.g. Classical Field Theory (Dover read here rjlexperts.com. In terms of de Broglie’s earlier calculations for the masses and momenta of photons, the mass and momentum constants for EM waves are not contradictory or confounding. It should be remembered that the photon of 20th century concepts was actually a collection of elementary light particles, i.e., EM oscillations OFDM for Underwater Acoustic Communications http://kronmagasinet.se/books/ofdm-for-underwater-acoustic-communications. Or, as in quantum common sense, did the physical wall-interaction affect the electron's probabilistic wave-function (which may exist only in our mathematics as a way to describe our knowledge), causing the wave-function to “collapse” at a specific location on the wall, thus triggering the detector+device and producing the cat's fate , e.g. Few-Body Problems in Particle, read here dh79.com?

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Adaptive Filters

The present work on the hydrogen atom clearly illustrates how the photoionization microscope images an electron orbital. In contrast, the authors’ previous work with photoionization microscopy found that orbital information can be obscured by multielectron effects [ 8 ]. Future research will try to understand how the electron-electron interaction manifests in photoionization microscopy Quantum Theory of Polymers as download online http://pv.ourdiscoveryschool.com/library/quantum-theory-of-polymers-as-solids. Notice that the change in speed of the waves inevitably produces a change in the wavelength. Interaction of Radiation and Matter: Semiclassical Theory Review of Basic Quantum Mechanics: Concepts, Postulates and Notation ( pdf ) Herod* *(c) Copyright 1994,1995,1996 by Evans M , e.g. Symmetry and Its Breaking in Quantum Field Theory (Physics Research and Technology) http://warholprints.com/library/symmetry-and-its-breaking-in-quantum-field-theory-physics-research-and-technology. It has nothing to do with quantum mechanics. It is simply that if we have a finite train, we cannot count the waves in it very precisely , e.g. A guide to Feynman diagrams in the many-body problem (European physics series) download pdf. PI; var bouncingBall1IsBigPoints = true; var bouncingBall1BigPointsAreaColor = 'yellow'; var bouncingBall1BigPointsLineColor = 'black'; var bouncingBall1BigPointsRadius = 5; // Pixels; var bouncingBall1AxisThickness = 3; var bouncingBall1XAxisColor = 'rgb(255, 0, 0)'; var bouncingBall1YAxisColor = 'rgb( 0, 255, 0)'; var bouncingBall1OriginColor = 'rgb(255, 255, 255)'; var bouncingBall1GridColor = 'rgb(200, 200, 200)'; var bouncingBall1GridThickness = 1; var bouncingBall1GridDeltaX = 1.0; var bouncingBall1GridDeltaY = 1.0; var bouncingBall1TurtleX = 0.0; var bouncingBall1TurtleY = 0.0; var bouncingBall1TurtleHeading = 0.0; var bouncingBall1TurtleIsPenDown = true; bouncingBall1SetupGraph = function() { bouncingBall1ClearGraph(); bouncingBall1DrawGrid(); bouncingBall1DrawAxes(); bouncingBall1DrawOrigin(); bouncingBall1SetAreaColor('yellow'); bouncingBall1SetLineThickness(2); bouncingBall1SetLineColor('black'); }; bouncingBall1ClearGraph = function() { bouncingBall1GC.clearRect(0, 0, bouncingBall1DeviceWidthPlus1, bouncingBall1DeviceHeightPlus1); }; bouncingBall1WorldToDeviceX = function(worldX) { return Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)); }; bouncingBall1WorldToDeviceY = function(worldY) { return Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin))); }; bouncingBall1SetLineThickness = function(thickness) { bouncingBall1GC.lineWidth = thickness; }; bouncingBall1SetLineCap = function(capStyle) // 'butt', 'round', or 'square' { bouncingBall1GC.lineCap = capStyle; }; bouncingBall1SetLineJoin = function(joinStyle) // 'round', 'bevel', or 'miter'' { bouncingBall1GC.lineJoin = joinStyle; }; bouncingBall1SetLineColor = function(color) { bouncingBall1GC.strokeStyle = color; }; bouncingBall1SetAreaColor = function(color) { bouncingBall1GC.fillStyle = color; }; bouncingBall1DrawPoint = function(worldX, worldY) { if(bouncingBall1IsBigPoints) { bouncingBall1GC.beginPath(); bouncingBall1GC.arc(Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin))), bouncingBall1BigPointsRadius, 0.0, bouncingBall1TwoPi, true); bouncingBall1GC.fill(); bouncingBall1GC.stroke(); } else { bouncingBall1GC.beginPath(); bouncingBall1GC.moveTo(Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin)))); bouncingBall1GC.lineTo(Math.round(bouncingBall1DevicePerWorldX * (worldX - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY - bouncingBall1WorldYMin)))); bouncingBall1GC.stroke(); } }; bouncingBall1DrawLineSegment = function(worldX1, worldY1, worldX2, worldY2) { bouncingBall1GC.beginPath(); bouncingBall1GC.moveTo(Math.round(bouncingBall1DevicePerWorldX * (worldX1 - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY1 - bouncingBall1WorldYMin)))); bouncingBall1GC.lineTo(Math.round(bouncingBall1DevicePerWorldX * (worldX2 - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (worldY2 - bouncingBall1WorldYMin)))); bouncingBall1GC.stroke(); }; bouncingBall1DrawArcLine = function(x, y, r, angle1, angle2) // World. { r = Math.round(bouncingBall1DevicePerWorldX * r); // x- and y-axes must be scaled the same. x = bouncingBall1WorldToDeviceX(x); y = bouncingBall1WorldToDeviceY(y); if(bouncingBall1IsAngleMeasurementInDegrees) { angle1 *= bouncingBall1RadiansPerDegree; } while(angle1 < 0.0) { angle1 += bouncingBall1TwoPi; } while(angle1 > bouncingBall1TwoPi) { angle1 -= bouncingBall1TwoPi; } if(bouncingBall1IsAngleMeasurementInDegrees) { angle2 *= bouncingBall1RadiansPerDegree; } while(angle2 < 0.0) { angle2 += bouncingBall1TwoPi; } while(angle2 > bouncingBall1TwoPi) { angle2 -= bouncingBall1TwoPi; } bouncingBall1GC.beginPath(); bouncingBall1GC.arc(x, y, r, angle1, -angle2, true); bouncingBall1GC.stroke(); }; bouncingBall1RectangleArea = function(x, y, width, height) // World. { bouncingBall1GC.fillRect(Math.round(bouncingBall1DevicePerWorldX * (x - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (y - bouncingBall1WorldYMin))), Math.round(bouncingBall1DevicePerWorldX * (width)), Math.round(bouncingBall1DevicePerWorldY * (height))); }; bouncingBall1RectangleLine = function(x, y, width, height) // World. { bouncingBall1GC.strokeRect(Math.round(bouncingBall1DevicePerWorldX * (x - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (y - bouncingBall1WorldYMin))), Math.round(bouncingBall1DevicePerWorldX * (width)), Math.round(bouncingBall1DevicePerWorldY * (height))); }; bouncingBall1RectangleClear = function(x, y, width, height) // World. { bouncingBall1GC.clearRect(Math.round(bouncingBall1DevicePerWorldX * (x - bouncingBall1WorldXMin)), Math.round(bouncingBall1DeviceHeight - (bouncingBall1DevicePerWorldY * (y - bouncingBall1WorldYMin))), Math.round(bouncingBall1DevicePerWorldX * (width)), Math.round(bouncingBall1DevicePerWorldY * (height))); }; bouncingBall1DrawAxes = function() { bouncingBall1SetLineThickness(bouncingBall1AxisThickness); bouncingBall1SetLineColor(bouncingBall1XAxisColor); bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, 0.0, bouncingBall1WorldXMax, 0.0); bouncingBall1SetLineColor(bouncingBall1YAxisColor); bouncingBall1DrawLineSegment(0.0, bouncingBall1WorldYMin, 0.0, bouncingBall1WorldYMax); bouncingBall1SetLineColor(bouncingBall1OriginColor); bouncingBall1DrawPoint(0.0, 0.0); }; bouncingBall1DrawOrigin = function() { bouncingBall1SetLineThickness(bouncingBall1OriginLineThickness); bouncingBall1SetLineColor(bouncingBall1OriginLineColor); bouncingBall1SetAreaColor(bouncingBall1OriginAreaColor); var x = bouncingBall1WorldToDeviceX(0) - 2; var y = bouncingBall1WorldToDeviceY(0) - 2; bouncingBall1GC.fillRect(x, y, 4, 4); bouncingBall1GC.strokeRect(x, y, 4, 4); }; bouncingBall1DrawGrid = function() { bouncingBall1SetLineThickness(bouncingBall1GridThickness); bouncingBall1SetLineColor(bouncingBall1GridColor); var x, y; for(x = 0.0; x <= bouncingBall1WorldXMax; x += bouncingBall1GridDeltaX) { bouncingBall1DrawLineSegment(x, bouncingBall1WorldYMin, x, bouncingBall1WorldYMax); } for(x = 0.0; x >= bouncingBall1WorldXMin; x -= bouncingBall1GridDeltaX) { bouncingBall1DrawLineSegment(x, bouncingBall1WorldYMin, x, bouncingBall1WorldYMax); } for(y = 0.0; y <= bouncingBall1WorldYMax; y += bouncingBall1GridDeltaY) { bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, y, bouncingBall1WorldXMax, y); } for(y = 0.0; y >= bouncingBall1WorldYMin; y -= bouncingBall1GridDeltaY) { bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, y, bouncingBall1WorldXMax, y); } }; bouncingBall1SetBounds = function(worldXMin, worldXMax, worldYMin, worldYMax) { bouncingBall1WorldXMin = worldXMin; bouncingBall1WorldXMax = worldXMax; bouncingBall1WorldYMin = worldYMin; bouncingBall1WorldYMax = worldYMax; bouncingBall1WorldPerDeviceX = (bouncingBall1WorldXMax - bouncingBall1WorldXMin) / (bouncingBall1DeviceWidth); bouncingBall1WorldPerDeviceY = (bouncingBall1WorldYMax - bouncingBall1WorldYMin) / (bouncingBall1DeviceHeight); bouncingBall1DevicePerWorldX = (bouncingBall1DeviceWidth) / (bouncingBall1WorldXMax - bouncingBall1WorldXMin); bouncingBall1DevicePerWorldY = (bouncingBall1DeviceHeight) / (bouncingBall1WorldYMax - bouncingBall1WorldYMin); }; bouncingBall1ShowBounds = function() { // TODO: Present graph bounds. }; bouncingBall1InitializeTurtle = function() { bouncingBall1TurtleX = 0.0; bouncingBall1TurtleY = 0.0; bouncingBall1TurtleHeading = 0.0; bouncingBall1TurtleIsPenDown = true; }; bouncingBall1PenUp = function() { bouncingBall1TurtleIsPenDown = false; }; bouncingBall1PenDown = function() { bouncingBall1TurtleIsPenDown = true; }; bouncingBall1SetH = function(a) { if(bouncingBall1IsAngleMeasurementInDegrees) { a *= bouncingBall1RadiansPerDegree; } while(a < 0.0) { a += bouncingBall1TwoPi; } while(a > bouncingBall1TwoPi) { a -= bouncingBall1TwoPi; } bouncingBall1TurtleHeading = a; }; bouncingBall1Home = function() { bouncingBall1TurtleX = 0.0; bouncingBall1TurtleY = 0.0; bouncingBall1TurtleHeading = 0.0; }; bouncingBall1Forward = function(d) { var turtleNewX; var turtleNewY; turtleNewX = bouncingBall1TurtleX + d * Math.cos(bouncingBall1TurtleHeading); turtleNewY = bouncingBall1TurtleY + d * Math.sin(bouncingBall1TurtleHeading); if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, turtleNewX, turtleNewY); } bouncingBall1TurtleX = turtleNewX; bouncingBall1TurtleY = turtleNewY; }; bouncingBall1Back = function(d) { bouncingBall1Forward(-d); }; bouncingBall1Right = function(a) { var turtleNewHeading; if(bouncingBall1IsAngleMeasurementInDegrees) { a *= bouncingBall1RadiansPerDegree; } turtleNewHeading = bouncingBall1TurtleHeading - a; while(turtleNewHeading < 0.0) { turtleNewHeading += bouncingBall1TwoPi; } while(turtleNewHeading > bouncingBall1TwoPi) { turtleNewHeading -= bouncingBall1TwoPi; } bouncingBall1TurtleHeading = turtleNewHeading; }; bouncingBall1Left = function(a) { bouncingBall1Right(-a); }; bouncingBall1SetX = function(x) { if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, x, bouncingBall1TurtleY); } bouncingBall1TurtleX = x; }; bouncingBall1SetY = function(y) { if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, bouncingBall1TurtleX, y); } bouncingBall1TurtleY = y; }; bouncingBall1SetXY = function(x, y) { if(bouncingBall1TurtleIsPenDown) { bouncingBall1DrawLineSegment(bouncingBall1TurtleX, bouncingBall1TurtleY, x, y); } bouncingBall1TurtleX = x; bouncingBall1TurtleY = y; }; bouncingBall1SetDegrees = function() { bouncingBall1IsAngleMeasurementInDegrees = true; }; bouncingBall1SetRadians = function() { bouncingBall1IsAngleMeasurementInDegrees = false; }; bouncingBall1Sine = function(a) { return Math.sin((bouncingBall1IsAngleMeasurementInDegrees)? (a * bouncingBall1RadiansPerDegree): a); }; bouncingBall1Cosine = function(a) { return Math.cos((bouncingBall1IsAngleMeasurementInDegrees)? (a * bouncingBall1RadiansPerDegree): a); }; bouncingBall1Tangent = function(a) { return Math.tan((bouncingBall1IsAngleMeasurementInDegrees)? (a * bouncingBall1RadiansPerDegree): a); }; bouncingBall1RandomX = function() { return bouncingBall1WorldXMin + (Math.random() * (bouncingBall1WorldXMax - bouncingBall1WorldXMin)); }; bouncingBall1RandomY = function() { return bouncingBall1WorldYMin + (Math.random() * (bouncingBall1WorldYMax - bouncingBall1WorldYMin)); }; ////////// // End: bouncingBall1 (x, y) graph canvas ////////// ////////// // Start: bouncingBall1 animation timeline ////////// var bouncingBall1Fps = 6; var bouncingBall1FrameIndex = 0; var bouncingBall1UserEventHandler = null; var bouncingBall1SystemEventHandler = null; var bouncingBall1Done = false; var bouncingBall1Timeout = null; var bouncingBall1TimeoutPeriod = 1000 / bouncingBall1Fps; bouncingBall1TimelineInitialize = function() { }; bouncingBall1Start = function() { clearTimeout(bouncingBall1Timeout); bouncingBall1Timeout = null; bouncingBall1UserEventHandler = null; bouncingBall1SystemEventHandler = null; bouncingBall1Done = false; bouncingBall1FrameIndex = 0; bouncingBall1SetUp(); bouncingBall1NextFrame(); }; bouncingBall1Resume = function() { bouncingBall1Done = false; bouncingBall1NextFrame(); }; bouncingBall1Pause = function() { clearTimeout(bouncingBall1Timeout); bouncingBall1Timeout = null; bouncingBall1Done = true; }; bouncingBall1Stop = function() { clearTimeout(bouncingBall1Timeout); bouncingBall1Timeout = null; bouncingBall1UserEventHandler = null; bouncingBall1SystemEventHandler = null; bouncingBall1Done = true; bouncingBall1SetDown(); }; bouncingBall1GotoFrame = function(frameIndex) { bouncingBall1FrameIndex = frameIndex; }; bouncingBall1SetUp = function() { }; bouncingBall1SetDown = function() { }; bouncingBall1NextFrame = function() { /* if(bouncingBall1UserEventHandler) { bouncingBall1UserEventHandler(); bouncingBall1UserEventHandler = null; } if(bouncingBall1SystemEventHandler) { bouncingBall1SystemEventHandler(); bouncingBall1SystemEventHandler = null; } */ bouncingBall1EveryFrameHandler(); //bouncingBall1SpecificFrameHandler(); if(!bouncingBall1Done) { bouncingBall1FrameIndex++; bouncingBall1Timeout = setTimeout(bouncingBall1NextFrame, bouncingBall1TimeoutPeriod); } }; bouncingBall1EveryFrameHandler = function() { // Every frame code goes here. }; bouncingBall1SpecificFrameHandler = function() { return; // Remove for use. //switch(bouncingBall1FrameIndex) //{ // case 0: // // // Specific frame code goes here. // // break; //} }; ////////// // End: bouncingBall1 animation timeline ////////// ////////// // Start: bouncingBall1 particle motion ////////// // Mass. var bouncingBall1M = 1.0; // X-axis. var bouncingBall1Xo = 0.0; var bouncingBall1Vxo = 0.0; var bouncingBall1Axo = 0.0; var bouncingBall1X1 = 0.0; var bouncingBall1X2 = 0.0; var bouncingBall1Vx1 = 0.0; var bouncingBall1Vx2 = 0.0; var bouncingBall1Ax1 = 0.0; var bouncingBall1Ax2 = 0.0; var bouncingBall1Fx = 0.0; var bouncingBall1XMin = -10.0; var bouncingBall1XMax = 10.0; // Y-axis. var bouncingBall1Yo = 0.0; var bouncingBall1Vyo = 0.0; var bouncingBall1Ayo = 0.0; var bouncingBall1Y1 = 0.0; var bouncingBall1Y2 = 0.0; var bouncingBall1Vy1 = 0.0; var bouncingBall1Vy2 = 0.0; var bouncingBall1Ay1 = 0.0; var bouncingBall1Ay2 = 0.0; var bouncingBall1Fy = 0.0; var bouncingBall1YMin = -10.0; var bouncingBall1YMax = 10.0; // Z-axis. //var bouncingBall1Zo = 0.0; //var bouncingBall1Vzo = 0.0; //var bouncingBall1Azo = 0.0; //var bouncingBall1Z1 = 0.0; //var bouncingBall1Z2 = 0.0; //var bouncingBall1Vz1 = 0.0; //var bouncingBall1Vz2 = 0.0; //var bouncingBall1Az1 = 0.0; //var bouncingBall1Az2 = 0.0; //var bouncingBall1Fz = 0.0; //var bouncingBall1ZMin = -10.0; //var bouncingBall1ZMax = 10.0; // Time interval per advance. var bouncingBall1Dt = 0.1; // Current time. var bouncingBall1T = 0.0; bouncingBall1ParticleMotionInitialize = function() { }; bouncingBall1SetOriginals = function() { bouncingBall1X1 = bouncingBall1X2 = bouncingBall1Xo; bouncingBall1Vx1 = bouncingBall1Vx2 = bouncingBall1Vxo; bouncingBall1Ax1 = bouncingBall1Ax2 = bouncingBall1Axo; bouncingBall1Y1 = bouncingBall1Y2 = bouncingBall1Yo; bouncingBall1Vy1 = bouncingBall1Vy2 = bouncingBall1Vyo; bouncingBall1Ay1 = bouncingBall1Ay2 = bouncingBall1Ayo; //bouncingBall1Z1 = bouncingBall1Z2 = bouncingBall1Zo; //bouncingBall1Vz1 = bouncingBall1Vz2 = bouncingBall1Vzo; //bouncingBall1Az1 = bouncingBall1Az2 = bouncingBall1Azo; bouncingBall1T = 0.0; }; bouncingBall1Advance = function() { // New position. bouncingBall1X2 = bouncingBall1X1 + (bouncingBall1Vx1 * bouncingBall1Dt) + (0.5 * bouncingBall1Ax1 * bouncingBall1Dt * bouncingBall1Dt); bouncingBall1Y2 = bouncingBall1Y1 + (bouncingBall1Vy1 * bouncingBall1Dt) + (0.5 * bouncingBall1Ay1 * bouncingBall1Dt * bouncingBall1Dt); //bouncingBall1Z2 = bouncingBall1Z1 + (bouncingBall1Vz1 * bouncingBall1Dt) + (0.5 * bouncingBall1Az1 * bouncingBall1Dt * bouncingBall1Dt); // New force. //bouncingBall1Fx = 1.0; //bouncingBall1Fy = 1.0; //bouncingBall1Fz = 1.0; // New acceleration. bouncingBall1Ax2 = bouncingBall1Ax1; bouncingBall1Ay2 = bouncingBall1Ay1; //bouncingBall1Az2 = bouncingBall1Az1; //bouncingBall1Ax2 = bouncingBall1Fx / bouncingBall1M; //bouncingBall1Ay2 = bouncingBall1Fy / bouncingBall1M; //bouncingBall1Az2 = bouncingBall1Fy / bouncingBall1M; // New Velocity. bouncingBall1Vx2 = bouncingBall1Vx1 + (((bouncingBall1Ax1 + bouncingBall1Ax2) / 2.0) * bouncingBall1Dt); bouncingBall1Vy2 = bouncingBall1Vy1 + (((bouncingBall1Ay1 + bouncingBall1Ay2) / 2.0) * bouncingBall1Dt); //bouncingBall1Vz2 = bouncingBall1Vz1 + (((bouncingBall1Az1 + bouncingBall1Az2) / 2.0) * bouncingBall1Dt); // X Bounce if(bouncingBall1X2 > bouncingBall1XMax) { //bouncingBall1X2 = (2 * bouncingBall1XMax) - bouncingBall1X2; bouncingBall1Vx2 = -bouncingBall1Vx2; } else if(bouncingBall1X2 < bouncingBall1XMin) { //bouncingBall1X2 = (2 * bouncingBall1XMin) - bouncingBall1X2; bouncingBall1Vx2 = -bouncingBall1Vx2; } // Y Bounce if(bouncingBall1Y2 > bouncingBall1YMax) { bouncingBall1Vy2 = -bouncingBall1Vy2; } else if(bouncingBall1Y2 < bouncingBall1YMin) { bouncingBall1Vy2 = -bouncingBall1Vy2; } // Z Bounce //if(bouncingBall1Z2 > bouncingBall1ZMax) //{ // bouncingBall1Vz2 = -bouncingBall1Vz2; //} //else if(bouncingBall1Z2 < bouncingBall1ZMin) //{ // bouncingBall1Vz2 = -bouncingBall1Vz2; //} // Tic-toc. bouncingBall1T += bouncingBall1Dt; }; bouncingBall1NewToOld = function() { // Position. bouncingBall1X1 = bouncingBall1X2; bouncingBall1Y1 = bouncingBall1Y2; //bouncingBall1Z1 = bouncingBall1Z2; // Velocity. bouncingBall1Vx1 = bouncingBall1Vx2; bouncingBall1Vy1 = bouncingBall1Vy2; //bouncingBall1Vz1 = bouncingBall1Vz2; // Acceleration. bouncingBall1Ax1 = bouncingBall1Ax2; bouncingBall1Ay1 = bouncingBall1Ay2; //bouncingBall1Az1 = bouncingBall1Az2; }; ////////// // End: bouncingBall1 particle motion ////////// // bouncingBall1_ main animation file var bouncingBall1TrailsX = new Array(); var bouncingBall1TrailsY = new Array(); var bouncingBall1TrailsColor = new Array(); var bouncingBall1NumTrails = 7; bouncingBall1TrailsColor[0] = '#222222'; bouncingBall1TrailsColor[1] = '#444444'; bouncingBall1TrailsColor[2] = '#666666'; bouncingBall1TrailsColor[3] = '#888888'; bouncingBall1TrailsColor[4] = '#aaaaaa'; bouncingBall1TrailsColor[5] = '#cccccc'; bouncingBall1TrailsColor[6] = '#eeeeee'; bouncingBall1Initialize = function() { bouncingBall1Xo = bouncingBall1RandomX(); bouncingBall1Vxo = 5.0 + Math.random() * 5.0; bouncingBall1Vxo = Math.random() < 0.5? bouncingBall1Vxo: -bouncingBall1Vxo; bouncingBall1Axo = 0.0; bouncingBall1Yo = bouncingBall1WorldYMin; bouncingBall1Vyo = 10.0 + Math.random() * 10.0; //bouncingBall1Vyo = Math.random() < 0.5? bouncingBall1Vyo: -bouncingBall1Vyo; bouncingBall1Ayo = -9.8; }; bouncingBall1SetUp = function() { bouncingBall1SetOriginals(); for(var i = 0; i < bouncingBall1NumTrails; i++) { bouncingBall1TrailsX[i] = bouncingBall1X1; bouncingBall1TrailsY[i] = bouncingBall1Y1; } }; bouncingBall1SetDown = function() { }; bouncingBall1EveryFrameHandler = function() { bouncingBall1ClearGraph(); bouncingBall1Advance(); bouncingBall1NewToOld(); bouncingBall1TrailsX.pop(); bouncingBall1TrailsX.unshift(bouncingBall1X1); bouncingBall1TrailsY.pop(); bouncingBall1TrailsY.unshift(bouncingBall1Y1); for(var i = 0; i < bouncingBall1NumTrails; i++) { bouncingBall1SetLineColor(bouncingBall1TrailsColor[i]); bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, bouncingBall1TrailsY[i], bouncingBall1WorldXMax, bouncingBall1TrailsY[i]); bouncingBall1DrawLineSegment(bouncingBall1TrailsX[i], bouncingBall1WorldYMin, bouncingBall1TrailsX[i], bouncingBall1WorldYMax); } for(var i = 0; i < bouncingBall1NumTrails - 1; i++) { bouncingBall1SetLineColor(bouncingBall1TrailsColor[i]); bouncingBall1DrawLineSegment(bouncingBall1TrailsX[i], bouncingBall1TrailsY[i], bouncingBall1TrailsX[i+1], bouncingBall1TrailsY[i+1]); } bouncingBall1SetLineColor('black'); bouncingBall1DrawLineSegment(bouncingBall1WorldXMin, bouncingBall1Y1, bouncingBall1WorldXMax, bouncingBall1Y1); bouncingBall1DrawLineSegment(bouncingBall1X1, bouncingBall1WorldYMin, bouncingBall1X1, bouncingBall1WorldYMax); bouncingBall1DrawPoint(bouncingBall1X1, bouncingBall1Y1); }; Welcome to the Physics Department of Zona Land Education ref.: Few-Body Problems in Physics '95: In memoriam Professor Paul Urban (Few-Body Systems) warholprints.com.

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