I got stuck at the equation 3.55 from Goldstein's Classical Mechanics textbook.

Problem 6. From the Goldstein's Classical Mechanics textbook, starting from equation (3.65) derive equation (3.67) by showing explicitly all the math steps. Starting from eq. 3.65 dr - 2mpz + E derive eq . 3. 67 + = 2 ( tan { + } tan ? ) since angular momentum, 1 , is conserved : 1 = mr'w = mr" do at dt = mr2 I de now recall eg 3.55 * = mk 12 ( 1 + 1 + 2ERE MK - Cos ( 0 - 0 ' ) ) mk r = - 1 + 1 1 + 2Ex CO MK2 Cos ( 0-0' ) mk / HECoS (0-0') = m Firm Cos (0- 0') combine w/ to get eq. 3. 66 1 + ecos ( 0 - 0')2