Notes on Projectile MotionIf we throw a ball at angle to the horizon randomly, what is the expected length of the trajectory? Catalan's constant appears in the answer. We are also interested in the expected average speed of the ball.
Physics in PerspectiveSalvia, S. (2014). Galileo's Machine: Late Notes on Free Fall, Projectile Motion, and the Force of Percussion (ca. 1638-1639). Physics in Perspective, 16(4), 440-460. https://doi.org/10.1007/s00016-014-0149-1...
Instead of solely using the traditional Lagrangian explicit technique based on Newton’s Second Law of Motion, the conservation of mass, momentum, and energy equations are utilized to determine particle response [47]. SPH still uses a Lagrangian formulation; however in the SPH implementation, the ...