Multiplebody

Multiplebody is a term used to describe a system comprising several interacting bodies connected through joints and constraints, analyzed within the framework of multibody dynamics. In such models, each body is treated as a rigid or, in some cases, deformable element with its own mass, inertia, and external forces. The overall motion is described in terms of generalized coordinates that capture the configuration of all bodies subject to kinematic constraints such as joints, gears, and contact.

The mathematical formulation typically starts from Newton-Euler or Lagrangian mechanics. A mass matrix M(q) along with constraint equations phi(q) = 0 define the dynamics. For rigid-body multibody systems, equations of motion take the form M(q) q̈ + C(q,q̇) + K(q) = τ + J^T λ, where τ are generalized applied forces, λ are constraint forces, and J is the Jacobian of the constraints. Inverse dynamics determine the forces needed to produce a desired motion, while forward dynamics compute accelerations from applied forces.

Applications span robotics (manipulators, legged robots), computer animation and game physics (character rigs and articulated figures), biomechanics (human joints and musculoskeletal models), and vehicle dynamics (suspension and drivetrain interactions). Numerical methods include rigid-body tree structures, Featherstone’s articulated-body algorithm, and various time-stepping or impulse-based integrators.

Limitations include modeling accuracy for flexible components, numerical stiffness, and the computational cost for large systems. Variants consider deformable bodies, contact mechanics, and frictional constraints. See also multibody dynamics, rigid body dynamics, articulated system, and constraint-based simulation.