Author: Pushkar Dave
The image below depicts the frames used for modeling the dynamics of the system. There are in total 11 frames, the World frame, the Box frame at the box's geometrical center and the Jack frame at the jack's geometrical center. To accurately check for impacts, there are 8 additional frames, 4 for each corner of the Jack, labelled r1 through r4 and 4 for each side of the box (located at the center of each side), labelled p1 through p4.
The configuration of the system is represented using 6 configuration variables xBox, yBox, thBox, xJack, yJack, thJack. The variables xBox, yBox, thBox represent the pose of the box with respect to the world frame and the variables xJack, yJack, thJack represent the pose of the jack with respect to the box frame.
The Euler Lagrange equations are used to solve for the equations of motion of the system. The impacts are modeled using impact update equations, which calculate the state of the system post impact.
A detailed article walking through the equations and steps will be up on my website soon.
