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