Rigid body dynamics

Rigid body dynamics studies how idealized bodies with fixed distances between their points move under applied forces and torques. It describes both translation of the center of mass and rotation about it.

Newton–Euler equations: Equations relating a body's external forces and torques to its linear and angular momentum changes. They provide the central equations of motion for translation and rotation.
Rotation matrix: An orthogonal matrix that represents a rotation while preserving lengths and angles. It maps body-fixed vectors into an inertial frame without changing their geometry.
Robot dynamics: The study of forces and motion in robotic mechanisms and their interaction with loads. Robot arms are linked rigid bodies whose inertial coupling shapes required actuator torques.
Rigid body: An idealized body whose distances between all pairs of points remain constant. This idealization defines the model whose motion the field analyzes.
Center of mass: The mass-weighted average position of a system, whose motion tracks its overall translation. External force determines the center of mass's translational acceleration.
Quaternion: A four-component algebraic representation commonly used to encode three-dimensional orientation. It avoids singularities that can occur when orientation is represented by Euler angles.
Spacecraft attitude control: Methods for orienting and stabilizing spacecraft using actuators and attitude measurements. Spacecraft orientation evolves according to torque and inertia in a near-torque-free environment.
Continuum mechanics: The study of matter modeled as continuously distributed material that can deform and flow. It replaces fixed internal distances with fields of deformation and stress.
Moment of inertia: A measure of how a body's mass is distributed relative to an axis of rotation. It determines how strongly angular acceleration responds to torque about an axis.
Euler angles: A set of three sequential rotations used to specify a body's orientation. They offer an intuitive orientation description but can become singular at gimbal lock.

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