The Euler-Poinaré principle is a reduced Hamilton's principle under Lie group framework. In this article, it is applied to derive a hybrid set of dynamical equations of rigid multibody systems, which include four parts: the classical Euler-Lagrange equations of rigid bodies in their translational coordinates of mass center; Euler-Poinaré equations via orientation matrices and their related angular velocities; the constraint equations due to different joints in Cartesian coordinates and Lie groups; and the reconstruction equations between special orthogonal groups and their Lie algebras. The generalized mass matrices of dynamical equations are constant, which is computationally efficient. All the equations can be constructed systematically and can be solved easily. The construction equations can be used to design Lie group integrators of multibody system dynamics. The procedure presented in this article can be extended easily to flexible multibody systems, systems with non-holonomic constraints, and so on.

Difficulty in emotional regulation is significantly correlated with depression. Depression is a psychological disease that seriously affects the physical and mental health of college students. Therefore, it is of great importance to develop diversified preventive interventions such as group impromptu music therapy (GIMT). The main purpose of this study was to evaluate the effect of GIMT on the improvement of emotional regulation ability and the reduction of depressive symptoms in college students. A 71 college students (36 in the experimental group and 35 in the control group) were recruited to carry out randomized controlled trial was used. The experimental group was intervened by GIMT. After the 4th week of intervention, follow-up and scale measurement were carried out. In the experimental group, emotional regulation difficulty scales (DERS) showed significant difference before and after GIMT, implying the improvement in the emotional regulation. But there was no significant improvement in the control group. In addition, the depressive symptoms of experimental group were relieved. All findings showed that GIMT can effectively improve college students’ emotional regulation and reduce depressive symptoms.