Mathematical Principles of Mechanics and Electromagnetism

Inhaltsverzeichnis

• of Part A.
• 1. Lagrangian Mechanics of Particles and Rigid Bodies.
• Section 1. Kinematics of Systems of Particles.
• Section 2. Kinematics of a Rigid Body.
• Section 3. Kinematics of Holonomic Systems of Particles and Rigid Bodies.
• Section 4. Dynamical Principles for Particles and Rigid Bodies.
• Section 5. Lagrange’s Equations for Constrained Systems.
• Section 6. Explicit Forms of Lagrange’s Equations.
• 2. Hamiltonian Systems in Phase Space.
• Section 7. Hamilton’s Principle.
• Section 8. Phase Space and Its Canonical Differential Forms.
• Section 9. The Legendre Transformation and the Hamiltonian System I: The Time-Independent Case.
• Section 10. The Legendre Transformation and the Hamiltonian System II: The Time-Dependent Case.
• Section 11. Contact Transformations and the Hamilton-Jacobi Equation.
• Section 12. The Hamilton-Jacobi Theory.
• Section 13. Huygens’ Principle for the Hamilton-Jacobi Equation 72 Appendix. Characteristics of a First-Order Partial Differential Equation.
• 3. Basic Principles of Continuum Mechanics.
• Section 14. Deformations and Motions.
• Section 15. Balance Principles.
• Section 16. Cauchy’s Postulate and the Stress Principle.
• Section 17. Field Equations.
• Section 18. Constitutive Equations.
• Section 19. Some Representation Theorems.
• Section 20. The Energy Principle for Hyperelastic Materials.
• Section 21. Internal Constraints.
• 4. Some Topics in the Statics and Dynamics of Material Bodies.
• Section 22. Homogeneous Simple Material Bodies.
• Section 23. Viscometric Flows of Incompressible Simple Fluids.
• Section 24. Universal Solutions for Isotropic Elastic Solids I: The Compressible Case.
• Section 25. Universal Solutions for Isotropic Elastic Solids II: The Incompressible Case.
• Section 26. Materially Uniform Smooth Elastic Bodies.
• Section27. Material Connections.
• Section 28. Noll’s Equations of Motion.
• Section 29. Inhomogeneous Isotropic Elastic Solid Bodies.
• Selected Reading for Part A.