Unformatted text preview: r to obtain a single firstorder equation for ݎሺݐሻ . 2. A single particle moves in the xyplane, in a general central potential V ( r ). (a) Using Newton’s 2 nd Law, write down the equations of motion for the particle in polar coordinates. (b) As in Problem 1(c), obtain firstorder equations for ݎሺݐሻ and ߠሺݐሻ. Show that the equations found in (a) follow from those in (b). (c) Obtain integral expressions for ݐሺݎሻ and ݐሺ ሻ. (d) Evaluate ݎሺݐሻ for the potential ܸ ൌ ଵ ଶ ݇ݎ ଶ . 3. Mathematica problem: (a) Use the command ParametricPlot to plot a circle parameterized by θ . The option AspectRatio>Automatic may be useful. (b) Plot a trajectory for the solution found in 2(d)....
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 Fall '08
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 mechanics, Atom, Angular Momentum, Force, Mass, firstorder equations, single firstorder equation

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