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In mechanical engineering, jerk, in addition to velocity and acceleration, is considered in the development of cam profiles because of tribological implications and the ability of the actuated body to follow the cam profile without chatter. [11] Jerk is often considered when vibration is a concern. A device that measures jerk is called a ...
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 = = =.
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 linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position x {\displaystyle x} , which varies with t {\displaystyle t} (time).
In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form (..., ¨, ˙,) = are sometimes called jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal ...
In an inertial frame of reference (subscripted "in"), Euler's second law states that the time derivative of the angular momentum L equals the applied torque: = For point particles such that the internal forces are central forces, this may be derived using Newton's second law.
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 ...
Eliminating the angular velocity dθ/dt from this radial equation, [47] ¨ = +. which is the equation of motion for a one-dimensional problem in which a particle of mass μ is subjected to the inward central force −dV/dr and a second outward force, called in this context the (Lagrangian) centrifugal force (see centrifugal force#Other uses of ...