Suppose that frame k' is moving with constant macroscopic velocity v with respect to frame k. a free particle moves with velocity in frame k. (a) show that the lagrangian l of the particle in frame k' can be represented by l' l+df/dt, where l is the lagrangian for the particle in frame k and f is a function of the particle's position f and time t (b) given this difference between l' and l, what can you say about the equation of motion in each frame?

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.