The Variational Principles of Mechanics |
Contents
THE BASIC CONCEPTS OF ANALYTICAL MECHANICS 1 The principal viewpoints of analytical mechanics | 3 |
Generalized coordinates | 6 |
The configuration space | 12 |
Copyright | |
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Common terms and phrases
analytical mechanics arbitrary auxiliary conditions boundary conditions C-point calculus of variations canonical equations canonical transformation configuration space consider const constant constraints curve d'Alembert's principle definite integral degrees of freedom derivatives differential form displacements dynamical Einstein elimination equations of motion equilibrium Euclidean expression extremum əqi force of inertia formulation fundamental geometry Hamiltonian function Hence holonomic impressed forces infinitesimal invariant Jacobi's principle kinetic energy Lagrange bracket Lagrangian equations Lagrangian function least action Let us assume line element mathematical mechanical paths mechanical system method minimizing moving Newtonian non-holonomic obtain optical P₁ parameter partial differential equation particle phase fluid phase space physical position coordinates potential energy principle of least problem of motion quantity rectangular coordinates reference system relation rheonomic Riemannian rigid body rotation scalar scleronomic solved stationary value Summary theorem theory tion vanish variation problem variational principles vector velocity virtual zero