Show that the shape (r(varphi)) for a central spring force ellipse takes the standard form (r^{2}=a^{2} b^{2}

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Show that the shape \(r(\varphi)\) for a central spring force ellipse takes the standard form \(r^{2}=a^{2} b^{2} /\left(b^{2} \cos ^{2} \varphi+a^{2} \sin ^{2} \varphi\right)\) if (in equation 7.37) we use the plus sign in the denominator and choose \(\varphi_{0}=\pi / 4\).

Data from equation 7.37

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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