Consider the Lagrangian function 1 L = m (x² + j² + ż²) + 16ý sin (x – t), where m is a positive constant, (x, y, z) are generalised coordinates and t is time. (i) Write down the generalised momenta Px, Py and pz. (ii) Does L have any cyclic coordinates? Justify your answer. (ii) Find the equations of motion. Can an analytic solution be found?
Consider the Lagrangian function 1 L = m (x² + j² + ż²) + 16ý sin (x – t), where m is a positive constant, (x, y, z) are generalised coordinates and t is time. (i) Write down the generalised momenta Px, Py and pz. (ii) Does L have any cyclic coordinates? Justify your answer. (ii) Find the equations of motion. Can an analytic solution be found?
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Transcribed Image Text:. Consider the Lagrangian function
1
L = m (i² + j? + ?) + 16ý sin (æ – t),
where m is a positive constant, (x, y, z) are generalised coordinates and t is time.
(i) Write down the generalised momenta pa, Py and Pz.
(ii) Does L have any cyclic coordinates? Justify your answer.
(ii) Find the equations of motion. Can an analytic solution be found?
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