Analytical Mech Homework Solutions 53

Analytical Mech Homework Solutions 53 - = i R sin t + R cos...

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ˆˆˆ sin cos iR t jR t jx iy ˆ ω =− Ω Ω + Ω Ω − + sin x yR t ′′ =− Ω Ω ± cos yx Rt +Ω ± (c) Let here uxi y =+ 1 i = ! sin cos y y R t i xiR t ′′′ =+ = ±±± iu ′ = y ix + sin cos Re it uiu R tiR ti += ΩΩ + = ± Try a solution of the form uA e B e −Ω ui A e i B e ′=− + Ω ± iu iA e iB e ωω () uiui B e +=+ ± so R B = + Ω Also at t the coordinate systems coincide so 0 = () () 00 uABx i y xR =+= + D R Ax RBx R =+−=+− + Ω DD so, R Ax + Ω D Thus, RR ux e e  +   D 5.7 The x, y frame of reference is attached to the Earth, but the x-axis always points away from the Sun. Thus, it rotates once every year relative to the fixed stars. The X,Y frame of reference is fixed inertial frame attached to the Sun. (a) In the x, y rotating frame of reference ( ) ( ) cos x tR ε = Ω− ( ) ( ) sin yt R t where R is the radius of the asteroid’s orbit
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