Consider a mass m moving in two dimensions with potential energy u (x, y) = 2 1 kr 2 , wherer 2 = x 2 + y 2 . write down the lagrangian, using coordinates x and y, and find the two lagrangeequations of motion. describe their solutions. [this is the potential energy of an ion in an "iontrap", which can be used to study the properties of individual atomic ions.]

1which body contains the majority of the mass in the solar system earth jupiter the moon the sun 2 what keeps the objects in the solar system such as planets orbiting around the sun the force of gravity the galaxy exerts on all objects within it including the solar system the great distance between the sun and the planets the sun's nuclear fusion which acts on each object the gravitational force between the sun and each object in the solar system