Physics Town

continues

SICM, 4.2

Posted on December 31, 2021 by rpflee

This was a virtual machine running the installation of MS-DOS 6.22 in the program VMware Player.

VMware Player was able to run virtual machines, but not to create one. Luckily, there was a website that helped me create virtual machine files. A virtual machine file is just a VMware-formatted text file. It defines the specifications of that virtual machine.

Running MS-DOS 6.22 was just for nostalgia. The real reason for learning virtual machines was to use the mechanics software library of the textbook “Structure and Interpretation of Classical Mechanics”. That library was available only for Linux.

— Me@2021-12-31 01:29:46 PM

Ex 1.22. Driven pendulum

Posted on December 31, 2021 by rpflee

Structure and Interpretation of Classical Mechanics

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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[guess]

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

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