IGNOU MTE 14 2018 - A particle is moving under a central attracting force F. Show that its

Question

A particle is moving under a central attracting force F. Show that its equations of motion can be written as

$\frac{d^2 u}{d\theta ^2} +u = \frac{F}{h^2 u^2}$ where $u = \frac{1}{r} and h = r^2 \frac{d\theta }{dt}$

15 Feb 2018

Answer :

Word Count : 373

To derive the equation of motion of a particle moving under a central attractive force $ F $, we'll start from the general equation of motion in polar coordinates and use the given relations. Let's break it down step by step: ### Step 1: General Equation of Motion in Polar Coordinates For a particle moving under a central force, the force is radial, so the equation of motion in polar coordinates (in terms of $ r $, the radial distance, and $ \theta $, the angular coordinate) is given by: \[ F =

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