The time-evolution of a physical system with one coordinate q is described by the La- grangian 1 L + aġ sin q sin t +b cos q, where a and b are constants. (a) Show that the corresponding Hamiltonian is 1 (p – a sin q sin t)² – b cos q. 2 H = - -
The time-evolution of a physical system with one coordinate q is described by the La- grangian 1 L + aġ sin q sin t +b cos q, where a and b are constants. (a) Show that the corresponding Hamiltonian is 1 (p – a sin q sin t)² – b cos q. 2 H = - -
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Is H a constant of motion?
Transcribed Image Text:The time-evolution of a physical system with one coordinate q is described by the La-
grangian
1
+ aġ sin q sint+b cos q,
L =
where a and b are constants.
(a) Show that the corresponding Hamiltonian is
1
Н
(p – a sin q sin t)² – b cos q.
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