We can integrate kinematic differential equations to determine both 1) where an object will be and 2) what orientation it will have after a specified amount of time. In this post I describe the mathematical procedure, and implement the solution in Python.
Using differential equations of motion (EOMs) governed by Newton’s 2nd law we can describe the kinematics and dynamics of objects in motion. In this post I describe how EOMs can be calculated and applied programmatically for a simple case of a falling and bouncing ball with one translational degree of freedom.
With a lack of complete basis vector representation for the two coordinate systems, there are an infinite number of rotation matrices, or axis-angle combinations that can be applied to achieve a desired vector mapping. However, here we define the constrained nature of the solution space.