This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations.

这项工作提出并研究了基于非扭转的旋转刚体的新模型。帧。这样的帧由三个相互正交的单位矢量组成，这些单位矢量围绕三个轴之一的旋转速率始终保持为零，因此由非完整约束表示。然后，通过采用两种描述来公式化相应的Lagrange-D'Alembert方程，第一种描述依赖于旋转和分裂方法，第二种描述依赖于约束指向矢。对于消失的外部力矩，我们证明了新模型具有守恒定律，即动能和两个非完整的力矩，它们与标准刚体模型所保存的完整的力矩大不相同。另外，我们提出了一类新的能量动量积分方案的专业化方案，该方案精确地保留了动能和非完整动量，从而复制了连续对应物。最后，我们给出了数值结果，这些结果表明了优良的守恒性质以及随时间离散的控制方程的精度。