By Dr. Vladimir G. Ivancevic, Tijana T. Ivancevic (auth.)
Human-Like Biomechanics is a finished creation into glossy geometrical the way to be used as a unified learn procedure in it seems that separate and quickly starting to be fields: mathematical biomechanics and humanoid robotics.
The publication includes six Chapters and an Appendix. the 1st bankruptcy is an advent, giving a short assessment of mathematical strategies for use within the textual content. the second one bankruptcy develops geometrical foundation of human-like biomechanics, whereas the 3rd bankruptcy develops its mechanical foundation, in most cases from generalized Lagrangian and Hamiltonian standpoint. The fourth bankruptcy develops topology of human-like biomechanics, whereas the 5th bankruptcy reports similar nonlinear keep watch over thoughts. The 6th bankruptcy develops covariant biophysics of electro-muscular stimulation. The Appendix comprises elements: classical muscular mechanics and glossy direction vital tools, that are either used often mostly textual content. the complete ebook relies at the authors’ personal study papers in human-like biomechanics.
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Additional resources for Human-Like Biomechanics: A Unified Mathematical Approach to Human Biomechanics and Humanoid Robotics
Now, given two topological spaces X and Y , a function (or, a map) f : X → Y is continuous if the inverse image of an open set in Y is an open set in X. The main general idea in topology is to study spaces which can be continuously deformed into one another, namely the idea of homeomorphism. If we have two topological spaces X and Y , then a map f : X → Y is called a homeomorphism iﬀ 1. f is continuous, and 2. There exists an inverse of f , denoted f −1 , which is also continuous. Deﬁnition (2) implies that if f is a homeomorphism then so is f −1 .
The set B is called the codomain of f , and denoted Cod f. The codomain is not to be confused with the range of f (A), which is in general only a subset of B. A function f : X → Y is called injective or one–to–one or an injection if for every y in the codomain Y there is at most one x in the domain X with f (x) = y. Put another way, given x and x in X, if f (x) = f (x ), then it follows that x = x . A function f : X → Y is called surjective or onto or a surjection if for every y in the codomain Cod f there is at least one x in the domain X with f (x) = y.
4 space–time coordinates); 2. 1 Local Tensorial Language of Human–Like Biomechanics 21 3. Formulate the action principle, as a vanishing variation of the AF, Ldx = δS[x] = δ δLdx = 0, with zero boundary ﬁeld variations; 4. Derive the Euler–Lagrangian equations of motion, using the vanishing δS functional derivative, δx i = 0, given by δS ∂L ≡ − ∂µ i δϕ ∂ϕi ∂L ∂µ ϕi . Now, once we have an acceptable AF, we can formulate the associated Feynman path integral, according to the procedures developed in Appendix.