6.946 Final Project

Dennis V. Perepelitsa 19 December 2006 Gerald Jay Sussman, Jack Wisdom Exercise 5.32: Hierarchical Jacobi coordinates (a) Canonical heliocentric coordinates The canonical heliocentric transformation singles out the center of mass of the system. The other coordinates are computed with respect to this coordinate. Specifically, the relationships between the elements of (x′0, . . . , x ′ n−1) and (x0, . . . , xn−1) are x′0 = X = ∑i=n−1 i=0 mixi ∑i=n−1 i=0 mi x′i = xi − x0, for i > 0 (1) We want to construct an F2-type generating function that relates the relationship between the transformed and original coordinates. Using x = ∂2F2(t;x; p ), we have