Dynamic Modeling of Sphere, Cylinder, Cone, and their Assembly

Dynamic simulation of revolved solids plays an important role in many fields. Aiming at the lacks of solutions in some key aspects, this study establishes governing equation of motion based on theory of variational inequality; designs a compatibility iteration algorithm for solving contact forces; deduces parametric equations of arbitrary cylinder and cone in three-dimensional space; provides corresponding analytical methods to identify contact points between bodies and to calculate volume integral over bodies; proposes a rotation matrix modification approach to conserve volume and shape of rigid body in the case of large rotation. The accuracy, availability, competence, robustness, and application prospects of the presented methodology are demonstrated by several interesting and challenging problems.