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Dynamics

The study of the causes of motion and changes in motion is dynamics. In other words, it is the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion. These are in contrast to kinematics, the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion.

Newton's laws

Newton described force as the ability to cause a mass to accelerate.

1. Newton's first law states that an object in motion will stay in motion unless a force is applied. This law deals with inertia, which is a property of matter that resists acceleration and depends only on mass.

2. Newton's second law states that force quantity is equal to mass multiplied by the acceleration (F = ma).

3. Newton's third law states that for every action, there is an equal but opposite reaction.

Multibody Dynamics

The systematic treatment of the dynamic behaviour of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics. The simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints.

Basically, the motion of bodies is described by their kinematic behaviour. The dynamic behaviour results from the equilibrium of applied forces and the rate of change of momentum. Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in robotics and vehicle dynamics. As an important feature, multibody system formalisms usually offer an algorithmic, computer-aided way to model, analyze, simulate and optimize the arbitrary motion of possibly thousands of interconnected bodies.

The following example shows a typical multibody system. It is usually denoted as slider-crank mechanism. The mechanism is used to transform rotational motion into translational motion by means of a rotating driving beam, a connection rod and a sliding body. In the present example, a flexible body is used for the connection rod. The sliding mass is not allowed to rotate and three revolute joints are used to connect the bodies. While each body has six degrees of freedom in space, the kinematical conditions lead to one degree of freedom for the whole system.

Rigid body dynamics

Rigid-body dynamics is the study of the motion of rigid bodies. Unlike particles, which move only in three degrees of freedom (translation in three directions), rigid bodies occupy space and have geometrical properties, such as a centre of mass, moments of inertia, etc., that characterize motion in six degrees of freedom (translation in three directions plus rotation in three directions). Rigid bodies are also characterized as being non-deformable, as opposed to deformable bodies. As such, rigid-body dynamics is used heavily in analyses and computer simulations of physical systems and machinery where rotational motion is important but material deformation does not have a significant effect on the motion of the system.