Second-order ODE systems
Since any second-order (or higher-order) ODE can be written as a system of first-order ODEs, psymple can be used to simulate complex composite differential equation systems of any order.
This collection of examples covers dynamics such as projectile motion and motion under gravity, where the position of an object is specified by second-order equations for its acceleration.
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Projectile motion
The motion of an object acting under multiple forces.
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The three body problem
A classical problem in celestial mechanics.