Broadly speaking, the study of the way systems change over time. There are two sorts of dynamics. One is linear (or Newtonian) dynamics in which there is a one-to-one, or proportional, relationship, between input to and output from the state (S) of a system, which can be schematically summarised as follows:
The other is non-linear dynamics in which there is no one-to-one, or proportional, relationship between input and output, such that a ‘small’ input may give rise to a ‘large’ output depending on the state of the system:
Furthermore, in such a system, the output can be a change in state:
There is another distinction to be made when talking about dynamics: forward dynamics and inverse dynamics. Forward (or direct) dynamics amounts to the problem of calculating or reproducing parameters of motion (e.g., acceleration) from known internal forces, in particular torques and reaction forces. The calculations involved can be quite challenging in the context of biological motion due to the variety of mechanical linkages in multibody systems, and so they have more widespread applications in robotics, computer games and animations. The reverse process is inverse dynamics: now the problem is to reconstruct internal forces from equations of motion, inertial forces of the body (e.g., mass, moment of inertia) and when needed known external forces (e.g., ground reaction forces). One of the main analytical tools in biomechanics (e.g., in the study of locomotion), it is now possible to calculate inverse (rigid-body) dynamics for up to 15-segment human body models in real time due to the high sampling frequencies (100 Hz and more) of contemporary motion capture systems. As with forward dynamics, it can prove to be a challenging task as in the case of inverse dynamics, for example, the co-activation of muscles can give rise to a suite of solutions that can be difficult to distinguish from the kinematics of the motion being studied. A third ‘way’ is hybrid dynamics: with forces known at some joints and particular kinematics at others, reconstruct the unknown forces and accelerations. Overcoming the problems associated with forward and inverse dynamics and finding solutions is a major and ongoing quest, particularly in biomechanics. In short, the distinction between forward and inverse dynamics can be summarized as follows: given the forces, work out the kinematics (forward dynamics), and given the kinematics, work out the forces (inverse dynamics).
See Antagonist muscle, Biomechanics, Dynamical system, Dynamical systems approaches, Force, Frequency, Inertia, Intrinsic dynamics, Kinematics, Kinetics, Linear dynamical systems, Mass, Moment of force, Moment of inertia (I), Newton’s laws of motion, Newtonian (or classical) systems, Non-linear dynamical systems, Non-linear dynamics, Torque