Dynamics/Solving Ordinary Differential Equations

Introduction

In dynamics and control, 2nd-order ordinary differential equations of a single variable are very common. For example, you may recall arguably the most famous example for a mass-spring-damper system given by the following:

$m\ddot{x}+b\dot{x}+kx=0$ ,

where $x$, $\dot{x}$, and $\ddot{x}$ describe the displacement, velocity, and acceleration of a system with a moving mass $m$, damping coefficient $b$, and a spring coefficient $k$.

To cast this system in the form of a state-space model/representation that involves a series of 1st-order differential equations

Topics

1. Kinematics
2. Newtonian Dynamics
3. Analytical Dynamics
4. Linearization
5. Solving Ordinary Differential Equations