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Lagrangians and Lagrangian Systems
Central Force Fields
9 other sections not shown
1-forms action variable action-angle action-angle variables adiabatic invariant angle angular momentum angular velocity antisymmetric arbitrary assume basis vectors calculation called canonical transformation center of mass classical mechanics components configuration space consider const constant constraint coordinate system coordinate transformation cross section curve defined depends derivative determined differential eigenvalues equations of motion equivalent Euler-Lagrange equations evaluate example Exercise explicit explicitly expression Figure force free particle frequency function given gives Hamilton equations Hamilton-Jacobi equation Hamiltonian harmonic oscillator Hence independent inertia infinitesimal integral integrand inverse kinetic energy Lagrangian linear manifold matrix momenta nonsingular nonzero notation obtain orbit orthogonal path parameter pendulum perturbation phase space plane Poisson bracket problem quantum mechanics result rotating frame scattering simple solution solve spacetime sphere spring Suppose tangent tensor theorem time-dependent two-dimensional vanishes variational principle write zero