2o ciclo problema mecanica clasica de la relatividad especial

[leonardo fabinchi]

Hola, estos son problemas del libro classical mechanics de H. Goldstein, del capitulo 7 sobre la mecanica clasica de la teoria especial de la relatividad. corresponden a 1) Derivaciones 7.9 2) ejercicios 7.25 Quisiera que me dieran pistas para solucionarlos, lo que me digan me sirve, cualquiera de los dos que me puedan ayudar.

1) A particle of rest mass $m$ charge $q$ and initial velociti $\vec{v_0}$ enters a uniform electric field $\vec{E}$ perpendicular to $\vec{v_0}$. Find the subsequent trajectory of the particle and show that it reduces to a parabola in the limit $c$ becomes infinite

2) A generalized potential suitable for use in a covariant Lagrangian for a single particle

$U=-A_{\lambda \nu}(x^{\,\mu})u^\lambda u^\nu$
where $A_{\lambda\nu}$ stands for a symmetric world tensor of the second rank and $u^\nu$ are the components of the world velocity. If the Lagrangian is

$\wedge=\frac{1}{2}mu_\nu u^\nu$

obtain the Lagrange equations of motion. What is the Minkowski force? Give the components of the force as observed in some Lorentz frame.


Mil gracias a quien me pueda ayudar asi sea con pistas.