**Unformatted text preview: **of the particle where . L = L In the next problem, it is proven that 2 2 2 2 1 mA E L + = where E is the total energy of the particle. Using simple algebra, one obtains . / 2 1 E A a-= But as shown in class, r A mv E / 2 2 1-= where here v is the speed of the particle at time t and r is the position of the particle at the same time t . Consequently, at time , t one obtains =-= 2 2 mv r A A a . 2 1 2- -v r 3. . 1 2 2 2 2 2 + × ⋅-= -× ⋅ -× = Ar A L v r A r A L r r r L r r L r & & & But . 2 m L = × ⋅ = × ⋅ r r L L r r & & Hence = -+ = -+ = r A mv mA L mr A v A L 2 2 1 2 2 2 2 2 2 1 2 1 . 2 1 2 2 mA E L +...

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- Spring '10
- BLUMAN
- Particle, Planet, Kepler's laws of planetary motion