final exam – written part - École Polytechnique de Montréal
final exam – written part - École Polytechnique de Montréal
final exam – written part - École Polytechnique de Montréal
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QUESTION 4 :<br />
A rigid pendulum consists of a mass m fixed at the end A of a rigid rod. This rod is of length L and of<br />
negligeable mass. The gravitational field is vertically oriented downward and constant in time. The end B of the<br />
rod (the pivot) is following a forced vertical movement, given by a function h(t), around the fixed point O. This<br />
configuration is illusrated on figure 1.<br />
Determine the Lagrangian and the Hamiltonian of this system, using the horizontal line passing through the<br />
fixed point O as the reference for the potential.<br />
Figure 1<br />
Examen général <strong>de</strong> synthèse - Partie écrite<br />
Vendredi 16 juin 2006<br />
Page 6 sur 11<br />
Dé<strong>part</strong>ement <strong>de</strong> génie physique
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