Answer Happy

(3.1) Consider a one-dimensional system which consists of two particles of masses m, and m₂, with coordinates x, and x₂(x₁ <x₂) interacting through gravity. Write down the expression for the Lagrangian of the system, and derive the Lagrangian form of the governing equations. (3.2) Consider the two-dimensional equivalent of the system described in Part (3.1), i.e. two particles of masses m, and m₂, with coordinates (x₁,₁) and (x₂,2) interacting through gravity. Write down the expressions for the kinetic and potential energies of the system. (3.3) Find the fixed points of the following dynamical system: $=0+ y² +w, w=o+y² +1₁ and examine their stability.