【摘要】 基于一个新的电矩张量~T(O)及旋转带电体的磁矩的矩阵表达方式,借助分析力学中关于刚体转动的欧拉角描述方法以及欧拉运动学方程,推导了旋转带电的电介质刚体在外加匀强磁场中的拉格朗日函数的一般形式,并在简单的四度对称条件下推导出具体的拉格朗日动力学方程组,发现并指出了其循环坐标及对应的守恒量,同时建立了其欧拉转动动力学方程.结果表明:拉格朗日动力学方程与欧拉动力学方程是各自完备、自洽并相互等价的,同时对具有均匀一致的荷质比的带电刚体,研究了其具有规则进动精确解的简单情形,并具体导出规则进动的角速度公式.更多还原

【Abstract】 Based upon a new charge moment tensor and the calculation rule of magnetic moment for a rotational charged body,and by means of Euler’s angular coordinates and Euler’s kinetic equation about a rotational rigid body in classical mechanics,the general Lagrangian and Euler’s dynamic equation of a charged dielectric rigid body under a uniform magnetic field have been derived.According to the test rule for a vector to make regular precession,one simple case of regular precession involved in a rotational charged rigid body in a uniform magnetic field is verified and the precession angular velocity is calculated.The concrete Lagrangian and Lagrange equations are also derived and discussed in detail for another symmetric case,whose corresponding invariants have also been found.更多还原