In: Physics
two masses m1 and m2 move under their mutual gravitation attraction in a uniform external gravitational field whose acceleration is g. Choose as coordinates the cartesian coordinates X, Y, Z, of the center of mass (taking Z in the direction of g), the distance r between m1 and m2, and the polar angles θ and φ which specify the direction of the line from m1 to m2. Write expressions for the kinetic energy, the six forces Q_x, ... ,Q_φ and the six momenta. Write out the six Lagrange equations of motion.