The Variational Principles of Mechanics, Volume 4, Issue 1970

action integral analytical mechanics arbitrary auxiliary conditions boundary conditions calculus calculus of variations canonical equations canonical transformation configuration space conservation consider const constant curve d'Alembert's principle definite integral degrees of freedom derivatives differential form displacement dynamical Einstein elimination equations of motion equilibrium Euclidean Euler expressed force of inertia formulation fundamental geometry grad Hamiltonian function Hence impressed forces infinitesimal invariant Jacobi's principle kinematical conditions kinetic energy Lagrange Lagrange bracket Lagrangian equations Lagrangian function least action line element Lorentz transformation mathematical mechanical paths mechanical system method momentum Newtonian obtain optical parameter partial differential equation particle phase fluid phase space physical position coordinates potential energy principle of least quantity rectangular coordinates reference system relation Riemannian rigid body rotation scalar stationary value tensor theorem theory tion vanish variational principle variational problem vector velocity virtual zero дх дхк