标题： 带电粒子在电磁场中的测地线 显示英文标题

标题： Geodesics of charged particle in electromagnetic field

摘要： 我们报告了关于带电粒子在外部电场和磁场中的运动计算。 对于具有非零牵引力和摩擦系数的斜面上运动的粒子的度规也进行了评估，适用于弱场情况。 我们以Finsler几何的形式得到了几何解。 我们证明了我们的解度规属于({\alpha }, \b{eta})-度规类，无论是否存在斜面运动的情况。 此外，外部磁场在度规中表现为一个额外的参数。 在磁场影响下的测地线喷射系数也已计算。 最后，我们估计了滑腻平面和圆锥体的指标和测地线。 显示英文摘要

摘要： We report calculations about the motion of a charged particle in an external electric and magnetic field. The metric for the particle moving on a slope with non-zero traction and coefficient of friction is also evaluated for weak fields. We have geometric solutions in terms of Finsler geometry. We show that our solution metrics belong to the ({\alpha}, \b{eta})-metric class for cases with and without motion on a slope. Further, the external magnetic field is manifested in an additional parameter in the metric. The geodesic spray coefficients under the influence of magnetic field have also been calculated. Finally, we have estimated the indicatrices and geodesics for slippery plane and cone.