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There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The equations of translational kinematics can easily be extended to planar rotational kinematics for constant angular acceleration with simple variable exchanges: = + = + = (+) = + (). Here θ i and θ f are, respectively, the initial and final angular positions, ω i and ω f are, respectively, the initial and final angular velocities, and α ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
Constant acceleration allows for the velocity vs. time graph to appear as straight lines, thus designating a relationship between displacement (ΔR), maximum velocity (v peak), acceleration (a), and time(Δt). The following equations show this. [6] [7] ΔR = 1 / 2 v peak Δt ΔR = 1 / 4 a(Δt) 2
There are three Kinematic equations for linear (and generally uniform) motion. These are v = u + at; v 2 = u 2 + 2as; s = ut + 1 / 2 at 2; Besides these equations, there is one more equation used for finding displacement from the 0th to the nth second. The equation is: = + ()
The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.
The mathematical description of motion, or kinematics, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates.
In the inertial frame, the differential equation is not always helpful in solving for the motion of a general rotating rigid body, as both I in and ω can change during the motion. One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant.