Mechanics in Differential Geometry

basis canonical equations canonical transformation chart components configuration space constant coordinates corresponding covector deduce defined denoted diffeomorphism differentiable manifold differentiable mapping differential equations differential form dx² dx³ element expressed exterior differential Əqi F₁ form of degree function Given Hamilton Hamilton-Jacobi equation Hamiltonian Hamiltonian vector field integral curve integral invariant introduce Lagrange equations Lagrangian Let us consider Lie derivative linear matrix mechanics motion equations neighborhood obtained one-form one-parameter orbit p-form P₁ perturbated phase space Poisson bracket problem Proof pull-back recall respect Riemannian solution symplectic Talpaert tangent vector tensor field tensor of type theorem variables vector bundle vector field vector space velocity written X₁ zero ӘР др хо