forwarddynamics

Forward dynamics is a method in physics and engineering for computing the accelerations of a system from its current state and the applied forces or torques. It is a fundamental tool in robotics, biomechanics, and physics-based animation, where the goal is to predict how a mechanism or body will move under prescribed inputs and external influences.

In multibody systems, the configuration is described by generalized coordinates q, with qdot and qddot denoting velocity and acceleration. The equations of motion can be written in the form M(q) qddot + C(q,qdot) + G(q) = tau + J^T f_ext, where M is the inertia (mass) matrix, C contains Coriolis and centrifugal terms, G accounts for gravity, tau are joint torques, and J^T f_ext represents external contact or interaction forces. Forward dynamics uses these equations to solve for qddot given q, qdot, tau, and any external forces, and then integrates to obtain qdot and q over time. This approach is essential for simulating motion under actuation and contact.

A key distinction is with inverse dynamics, which computes the required torques given a desired trajectory (q, qdot, qddot). Forward dynamics is thus the step from control inputs to motion, making it central to model-based control, motion planning, and dynamic animation. In practice, solving forward dynamics can involve numerical methods for large, sparse systems, and may incorporate contact, friction, and constraints through penalty methods, complementarity formulations, or constraint stabilization techniques.

See also: inverse dynamics, multibody dynamics, physics-based simulation, robotics control.