The discussion focuses on transforming the ordinary differential equation (ODE) given by $$U' = -\frac{mgb}{\sin^2\theta} - \frac{Mgb\cos\theta}{\sin^2\theta}$$ into a system of equations. The equation can be expressed as $$U' = \frac{gb}{\sin^2\theta}(m - M\cos\theta)$$, which highlights the dependence on the variable $\theta$. The primary goal is to identify the fixed points of this system, prompting the need for transformation to facilitate analysis.
PREREQUISITESMathematicians, physicists, and engineers interested in dynamical systems, particularly those working with ordinary differential equations and fixed point analysis.
dwsmith said:Can this be written as a system since it only has theta?
$$
U' = -\frac{mgb}{\sin^2\theta} - \frac{Mgb\cos\theta}{\sin^2\theta} = \frac{gb}{\sin^2\theta}(m - M\cos\theta).
$$