DoublePendulum

Systems · Continuous · Physical systems

Dimension: 4

Equations

\[ \begin{aligned} \dot{y_{0}} &= \frac{6 \left(2 y_{2} - 3 y_{3} \cos{\left(y_{0} - y_{1} \right)}\right)}{d^{2} m \left(16 - 9 \cos^{2}{\left(y_{0} - y_{1} \right)}\right)} \\ \dot{y_{1}} &= \frac{6 \left(- 3 y_{2} \cos{\left(y_{0} - y_{1} \right)} + 8 y_{3}\right)}{d^{2} m \left(16 - 9 \cos^{2}{\left(y_{0} - y_{1} \right)}\right)} \\ \dot{y_{2}} &= - 0.5 d^{2} m \left(\frac{29.46 \sin{\left(y_{0} \right)}}{d} + \frac{36 \left(2 y_{2} - 3 y_{3} \cos{\left(y_{0} - y_{1} \right)}\right) \left(- 3 y_{2} \cos{\left(y_{0} - y_{1} \right)} + 8 y_{3}\right) \sin{\left(y_{0} - y_{1} \right)}}{d^{4} m^{2} \left(16 - 9 \cos^{2}{\left(y_{0} - y_{1} \right)}\right)^{2}}\right) \\ \dot{y_{3}} &= - 0.5 d^{2} m \left(\frac{29.46 \sin{\left(y_{1} \right)}}{d} - \frac{36 \left(2 y_{2} - 3 y_{3} \cos{\left(y_{0} - y_{1} \right)}\right) \left(- 3 y_{2} \cos{\left(y_{0} - y_{1} \right)} + 8 y_{3}\right) \sin{\left(y_{0} - y_{1} \right)}}{d^{4} m^{2} \left(16 - 9 \cos^{2}{\left(y_{0} - y_{1} \right)}\right)^{2}}\right) \end{aligned} \]

Parameters

parameter	default
d	1.0
m	1.0

Usage

import tsdynamics as ts

sys = ts.DoublePendulum()
traj = sys.integrate(final_time=100.0, dt=0.01)

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