Show that lagrange’s equations in the form of eqs. (1.53) can also be written as ∂t˙ ∂ ˙ q j − 2 ∂t ∂q j = q j . these are sometimes known as the nielsen form of the lagrange equations.

it would be kevlar ^^

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.