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Analytical Mech Homework Solutions 69

# Analytical Mech Homework Solutions 69 - For r = a and the...

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For r a θ = , and the force to be central, try n bt θ = ( ) ( ) 2 2 2 2 2 2 2 2 1 n n f m ab n t ab n n t θ = + For a central field … ( ) 0 f θ = ( ) 2 1 n n + = 0 1 3 n = 1 3 bt θ = 6.14 (a) Calculating the potential energy ( ) 2 3 5 4 dv a f r k dr r r = = − + Thus, 2 2 4 2 4 a V k r r = − + The total energy is … 2 2 2 2 2 1 2 1 1 9 9 0 2 4 2 2 4 k k E T V v k a a a a = + = + = = D D D Its angular momentum is … 2 2 2 4 9 2 k l a v constant r 2 θ = = = = D ± Its KE is … ( ) 2 2 2 2 2 2 2 2 2 4 1 1 1 2 2 2 dr dr l T r r r r d d θ θ θ θ = + = + = + ± ± ± r The energy equation of the orbit is … 2 2 2 2 4 2 1 2 0 2 4 dr l a T V r k d r r θ
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