Chapter 3: Problem 11
A particle of mass \(m\) is constrained to move under gravity on the surface of a smooth right circular cone of semi-vertical angle \(\pi / 4\). The axis of the cone is vertical, with the vertex downwards. Find the equations of motion in terms of \(z\) (the height above the vertex) and \(\theta\) (the angular coordinate around the circular cross-sections). Show that $$ \dot{z}^{2}+\frac{h^{2}}{2 z^{2}}+g z=E $$ where \(E\) and \(h\) are constant. Sketch and interpret the trajectories in the \(z, \dot{z}\)-plane for a fixed value of \(h\).
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.