Classical Mechanics with Mathematica®

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overv...

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Hlavní autor: Romano, Antonio (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing, 2018.
Vydání:2nd ed. 2018.
Edice:Modeling and Simulation in Science, Engineering and Technology,
Témata:
Mathematical physics.
Differential geometry.
Mechanics.
Physics.
ISBN:9783319775951
ISSN:2164-3679
On-line přístup: Získat plný text
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Obsah:
  • Part I: Introduction to Linear Algebra and Differential Geometry
  • Vector Spaces and Linear Maps
  • Tensor Algebra
  • Skew-Symmetric Tensors and Exterior Algebra
  • Euclidean and Symplectic Vector Spaces
  • Duality and Euclidean Tensors
  • Differentiable Manifolds
  • One-Parameter Groups of Diffeomorphisms
  • Exterior Derivative and Integration
  • Absolute Differential Calculus
  • An Overview of Dynamical Systems
  • Part II: Mechanics
  • Kinematics of a Point Particle
  • Kinematics of Rigid Bodies
  • Principles of Dynamics
  • Dynamics of a Material Point
  • General Principles of Rigid Body Dynamics
  • Dynamics of a Rigid Body
  • Lagrangian Dynamics
  • Hamiltonian Dynamics
  • The Hamilton-Jacobi Theory
  • Completely Integrable Systems
  • Elements of Statistical Mechanics of Equilibrium
  • Impulsive Dynamics
  • Introduction to Fluid Mechanics
  • An Introduction to Celestial Dynamics
  • One-Dimensional Continuous Systems
  • An Introduction to Special Relativity
  • Variational Calculus with Applications
  • Appendix A: First-Order PDEs
  • Appendix B: Fourier Analysis
  • Index.

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