The Lagrangian forthe Kepler problem is given by L = 12[ dot r^2 + r^2dot ^2 ] + r( > 0 ) where, ( r, ) denotes the polar coordinates and mass of the particle is unity, then

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Classical Mechanics

The Lagrangian forthe Kepler problem is given by $$L = \frac{1}{2}\left[ {{{\dot r}^2} + {r^2}{{\dot \theta }^2}} \right] + \frac{\mu }{r}\,\,\,\,\,\,\,\left( {\mu > 0} \right)$$
where, $$\left( {r,\,\theta } \right)$$ denotes the polar coordinates and mass of the particle is unity, then

A) $${p_\theta } = 2{r^2}\dot \theta $$ B) $${p_r} = 2\dot r$$ C) the angular momentum of the particle about the centre of attraction is a constant D) the total energy of the particle is time dependent

Answer & Solution

Correct Answer: Option C

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The Lagrangian forthe Kepler problem is given by L = frac...

The Lagrangian forthe Kepler problem is given by $$L = \frac{1}{2}\left[ {{{\dot r}^2} + {r^2}{{\dot \theta }^2}} \right] + \frac{\mu }{r}\,\,\,\,\,\,\,\left( {\mu > 0} \right)$$ where, $$\left( {r,\,\theta } \right)$$ denotes the polar coordinates and mass of the particle is unity, then

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Related Questions on Classical Mechanics

The Lagrangian forthe Kepler problem is given by $$L = \frac{1}{2}\left[ {{{\dot r}^2} + {r^2}{{\dot \theta }^2}} \right] + \frac{\mu }{r}\,\,\,\,\,\,\,\left( {\mu > 0} \right)$$
where, $$\left( {r,\,\theta } \right)$$ denotes the polar coordinates and mass of the particle is unity, then