If I have two points on a Cartesian plane, and I know that they are connected by a cycloid, then how do I find the equation for that cycloid? For background information, I have been playing around ...
I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and ...
Let $r=f(\theta)$ be a smooth, $2\pi$-periodic function, representing a curve star-shaped with respect to the origin. Maybe something like this: ...
What is the path of a projectile under an inverse-cube gravity law? Imagine that the law of gravity was changed overnight from $F(r) = G m_1 m_2 / r^2$ to $F(r) = G' m_1 m_2 / r^3$. To be ...