Solution Found!
Although the main topic of this chapter is the motion of
Chapter 8, Problem 8.2(choose chapter or problem)
Although the main topic of this chapter is the motion of two particles subject to no external forces, many of the ideas [for example, the splitting of the Lagrangian into two independent pieces = Zan as in Equation (8.13)] extend easily to more general situations. To illustrate this, consider the following: Two masses m1 and m2 move in a uniform gravitational field g and interact via a potential energy U(r). (a) Show that the Lagrangian can be decomposed as in (8.13). (b) Write down Lagrange's equations for the three CM coordinates X, Y, Z and describe the motion of the CM. Write down the three Lagrange equations for the relative coordinates and show clearly that the motion of r is the same as that of a single particle of mass equal to the reduced mass it, with position r and potential energy U(r).
Questions & Answers
QUESTION:
Although the main topic of this chapter is the motion of two particles subject to no external forces, many of the ideas [for example, the splitting of the Lagrangian into two independent pieces = Zan as in Equation (8.13)] extend easily to more general situations. To illustrate this, consider the following: Two masses m1 and m2 move in a uniform gravitational field g and interact via a potential energy U(r). (a) Show that the Lagrangian can be decomposed as in (8.13). (b) Write down Lagrange's equations for the three CM coordinates X, Y, Z and describe the motion of the CM. Write down the three Lagrange equations for the relative coordinates and show clearly that the motion of r is the same as that of a single particle of mass equal to the reduced mass it, with position r and potential energy U(r).
ANSWER:Step 1 of 8
(a)
