Implementing Classical Mechanics
Overview
Computing Newtons Equations
{% y(t_0 + \Delta t) \approx y(t_0) + dy(t_0)/ dt \times \Delta t %}
which can be justified using a
Taylors Series approximation.
An approximation to Newtons equations can be modeled through a matrix equation.
(see
Linear Algebra corner)
{%
\begin{bmatrix}
\ddot{x}(t+1) \\
\dot{x}(t+1) \\
x(t+1) \\
\end{bmatrix}
=
\begin{bmatrix}
0 & 0 & -k \\
\Delta t & 1 & 0\\
0 & \Delta t & 1 \\
\end{bmatrix}
\begin{bmatrix}
\ddot{x}(t) \\
\dot{x}(t) \\
x(t) \\
\end{bmatrix}
%}
Examples
