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Unformatted text preview: Use your solution for an ellipse to determine a formula for the energy in terms of the semi-major axis a . b) (10 pts) Consider scattering by a central force V(r). Determine an expression for the time as a function of radial distance r assuming that t=0 pertains to the distance of closest approach, 3) (30 points) a) (20 pts) Find the principal moments of inertia and the principal axes for the following system: I xx = a I yy = a I zz = b I xy = c ( c < a ) I xz = I yz = 0 b) (10 pts) Express the unit vectors in the principal axis system in terms of the unit vectors in the initial axis system by a rotation matrix with specific angles. Some Basic Equations d dt " L q # L q = Q k = " # $ % & f q k h = q j j " L q j $ L dh dt = " L t l = mr 2 " V = V + l 2 2 mr 2 l = mvb T = m 2 r 2 + r 2 2 ( ) = $ 2 %...
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