Ex 1.22. Driven pendulum

Structure and Interpretation of Classical Mechanics

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Show that the Lagrangian (1.89) can be used to describe the driven pendulum, where the position of the pivot is a specified function of time: Derive the equations of motion using the Newtonian constraint force prescription, …

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\displaystyle{ \begin{aligned}  m \ddot{y} &= F \cos \theta - mg \\  m \ddot{x} &= - F \sin \theta \\  \end{aligned}}

\displaystyle{ \begin{aligned}  m \ddot{y} &= F \frac{y_s - y}{l} - mg \\  m \ddot{x} &= - F \frac{x - x_s}{l} \\  \sqrt{(x_s - x)^2 + (y_s - y)^2} &= l \\  \end{aligned}}

[guess]

— Me@2021-12-30 09:25:17 AM

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