Several examples of pendulum problem from classical mechanics. I expect to add more examples over time.
17-11 Classic Pendulum 05-16-16
The equation for the classical pendulum is derived and solved. Various changes of variable and manipulations are facilitated by using Mathematica. The classic solution in terms of elliptic functions is generated. A formula for the nonlinear dependence of pendulum period on displacement amplitude is calculated and compared against a numerical calculation.
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17-12 Double Pendulum Morin 6.19 5-25-16
Some calculations related to a double pendulum are performed. The analysis is guided by problem 6.19 of Morin’s Introduction to Classical Mechanics. The Euler-Lagrange equations are derived and solved. An eigenmode analysis if performed for perturbations about the equilibrium state.
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17-13 Spherical Pendulum 06-09-16
Some calculations related to a spherical pendulum are performed. The Euler-Lagrange equations are derived and solved. Those equations are numerically solved and an animation of the pendulum motion is shown. The tractable special case of a conical pendulum is solved and some analytical estimates of precession are compared with numerical results.
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17-14 Inverted Pendulum - Morin 6.5 07-16-16
Some calculations related to a driven inverted pendulum are performed. The analysis is guided by problem 6.5 of Morin’s Introduction to Classical Mechanics. The Euler-Lagrange equations are derived and solved. Attention is focused on the oscillatory motion of the driven pendulum about vertical.
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