Dynamics (mechanics)

For dynamics as the mathematical analysis of the motion of bodies as a result of impressed forces, see analytical dynamics.

Dynamics is a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.

Principles

Generally speaking, researchers involved in dynamics study how a physical system might develop or alter over time and study the causes of those changes. In addition, Newton established the fundamental physical laws which govern dynamics in physics. By studying his system of mechanics, dynamics can be understood. In particular, dynamics is mostly related to Newton's second law of motion. However, all three laws of motion are taken into account because these are interrelated in any given observation or experiment.

Linear and rotational dynamics

The study of dynamics falls under two categories: linear and rotational. Linear dynamics pertains to objects moving in a line and involves such quantities as force, mass/inertia, displacement (in units of distance), velocity (distance per unit time), acceleration (distance per unit of time squared) and momentum (mass times unit of velocity). Rotational dynamics pertains to objects that are rotating or moving in a curved path and involves such quantities as torque, moment of inertia/rotational inertia, angular displacement (in radians or less often, degrees), angular velocity (radians per unit time), angular acceleration (radians per unit of time squared) and angular momentum (moment of inertia times unit of angular velocity). Very often, objects exhibit linear and rotational motion.

For classical electromagnetism, it is Maxwell's equations that describe the dynamics. And the dynamics of classical systems involving both mechanics and electromagnetism are described by the combination of Newton's laws, Maxwell's equations, and the Lorentz force.

Force

Main article: Force

From Newton, force can be defined as an exertion or pressure which can cause an object to accelerate. The concept of force is used to describe an influence which causes a free body (object) to accelerate. It can be a push or a pull, which causes an object to change direction, have new velocity, or to deform temporarily or permanently. Generally speaking, force causes an object's state of motion to change.

Newton's laws

Main article: Newton's laws of motion

Newton described force as the ability to cause a mass to accelerate. His three laws can be summarized as follows:

1. First law: If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.
2. Second law: The rate of change of linear momentum P of an object is equal to the net force F_net, i.e., dP/dt = F_net.
3. Third law: When a first body exerts a force F₁ on a second body, the second body simultaneously exerts a force F₂ = −F₁ on the first body. This means that F₁ and F₂ are equal in magnitude and opposite in direction.

Newton's Laws of Motion are valid only in an inertial frame of reference

See also

• Multibody dynamics
• Rigid body dynamics
• Analytical dynamics