- #1
gabu
- 5
- 0
Greetings.
So... let us consider a particle moving in the yz plane, coming from the infinite towards a region were a gravitational potential is appreciable. The Lagrangian of the system is
\mathcal{L} = \frac{1}{2}\mu (\dot{r}^2+r^2{\dot \phi}^2) + \frac{G\,m\,M}{r}
where \mu is the reduced mass and r is the relative distance between the scattered particle and the particle generating the gravitational potential. From this Lagrangian we take that the quantity
L = m\,r\,v
is conserved, right? Now, from the angular momentum vector we have,
\vec{L} = m\,(y\,\dot{z} - z\,\dot{y})
and |\vec{L}| = m\,r\,v\,\sin\theta where \theta is the angle between r and v.
So... my problem is, the angular momentum is then only conserved when r and v are orthogonal? So, it doesn't really apply to scattering, only for orbiting particles?
Thank you very much.
So... let us consider a particle moving in the yz plane, coming from the infinite towards a region were a gravitational potential is appreciable. The Lagrangian of the system is
\mathcal{L} = \frac{1}{2}\mu (\dot{r}^2+r^2{\dot \phi}^2) + \frac{G\,m\,M}{r}
where \mu is the reduced mass and r is the relative distance between the scattered particle and the particle generating the gravitational potential. From this Lagrangian we take that the quantity
L = m\,r\,v
is conserved, right? Now, from the angular momentum vector we have,
\vec{L} = m\,(y\,\dot{z} - z\,\dot{y})
and |\vec{L}| = m\,r\,v\,\sin\theta where \theta is the angle between r and v.
So... my problem is, the angular momentum is then only conserved when r and v are orthogonal? So, it doesn't really apply to scattering, only for orbiting particles?
Thank you very much.