Question

a) A small block of mass m is confined to move on the inside surface of a cone defined by z = aρ, where (ρ, φ, z) give its position in cylindrical coordinates. The block slides without friction along the surface and feels the gravitational force, which is directed in the negative z direction. a. Write down the Lagrangian for the system in terms of the coordinates ρ and φ

b) Obtain the Lagrange equations of motion for the coordinate

c) Obtain the first integral of the equation from part (b) and give the physical interpretation of this result

d) Obtain the Lagrange equations of motion for the coordinate ρ.

Answer 1