The standard vector treatment of central force motion is facilitated by representing vectors with complex numbers. When a radius vector r is represented by the polar form r exp (iθ), no vector theorems are required to generate the equations of motion. The formalism is applied to establish conservation of energy and angular momentum. A third conserved quantity, a complex number, is introduced for the inverse‐square law. The orbit expression r=r(θ) follows from this quantity without formulating or solving a differential equation.
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© 1990 American Association of Physics Teachers.
1990
American Association of Physics Teachers
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