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In motion control, the design focus is on straight, linear motion, with the need to move a system from one steady position to another (point-to-point motion). The design concern from a jerk perspective is vertical jerk; the jerk from tangential acceleration is effectively zero since linear motion is non-rotational.
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The Lorentz self-force derived for non-relativistic velocity approximation , is given in SI units by: = ˙ = ˙ = ˙ or in Gaussian units by = ˙. where is the force, ˙ is the derivative of acceleration, or the third derivative of displacement, also called jerk, μ 0 is the magnetic constant, ε 0 is the electric constant, c is the speed of light in free space, and q is the electric charge of ...
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.
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]
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Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk. See motion graphs and derivatives. A large number of fundamental equations in physics involve first or second time derivatives of quantities. Many other fundamental quantities in science are time derivatives of one another: