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A simple pendulum consists of a particle of mass m on an inextensible massless string of length &. The kinetic energy of the system in Cartesian coordinates is given by T=m (x + y²) where x and y may also be expressed in their polar coordinates format as x = { sin 0, and y = - { cos 0 respectively.

A simple pendulum consists of a particle of mass m on an inextensible massless string of length &. The kinetic energy of the system in Cartesian coordinates is given by T=m (x + y²) where x and y may also be expressed in their polar coordinates format as x = { sin 0, and y = - { cos 0 respectively.

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From the Euler-Lagrange equation of motion: = 0, aq dt aqk Show that the equation of motion for this system is given by:
Transcribed Image Text:From the Euler-Lagrange equation of motion: = 0, aq dt aqk Show that the equation of motion for this system is given by:
A simple pendulum consists of a particle of mass m on an inextensible massless string of length ? The kinetic energy of the system in Cartesian coordinates is given by T=m (x2 + y?) where x and y may also be expressed in their polar coordinates format as x { sin 0, and y = -l cos 0 respectively.
Transcribed Image Text:A simple pendulum consists of a particle of mass m on an inextensible massless string of length ? The kinetic energy of the system in Cartesian coordinates is given by T=m (x2 + y?) where x and y may also be expressed in their polar coordinates format as x { sin 0, and y = -l cos 0 respectively.
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