PHY354H1 Study Guide - Final Guide: Codex Corbeiensis I, Precession, Poisson Bracket
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Any s quantities q1, q2, , qs which completely de ne the position of a system with s degrees of freedom are the generalized coordinates of the system, while their derivatives qs are the system"s generalized velocities. L = t v , where t is the kinetic energy and v is the potential energy of a system. Note that the lagrangian is invariant under scalings and the addition of a total time deriva- tive (i. e. l l + df (q, t)/dt. It will probably be useful to recall the free-particle lagrangians for cartesian, cylindrical, and spherical coordinate systems: 2 m(cid:0) x2 + y2 + z2(cid:1) , 2 m(cid:16) r2 + r2 2 + z2(cid:17) , 2 m(cid:16) r2 + r2 2 + r2 2 sin2 (cid:17) An equation derived from the euler-lagrange equation is known as an equation of motion. If the problem involves several di erent coordinates, we apply the euler-lagrange equation to each coordinate.
