Search results
Results from the WOW.Com Content Network
Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement [3] [4] (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement.
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 = = =.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
Let t be a time-like parameter and consider a time-dependent domain Ω with a smooth surface boundary S. Let F be a time-dependent invariant field defined in the interior of Ω. Then the rate of change of the integral ∫ Ω F d Ω {\displaystyle \int _{\Omega }F\,d\Omega }
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 time derivatives of the generalized coordinates are called the generalized velocities, and for each particle the transformation of its velocity vector, the total derivative of its position with respect to time, is ˙ =, = = ˙ +.
derivative of position with respect to time (dx/dt, velocity) has dimension T −1 L—length from position, time due to the gradient; the second derivative (d 2 x/dt 2 = d(dx/dt) / dt, acceleration) has dimension T −2 L. Likewise, taking an integral adds the dimension of the variable one is integrating with respect to, but in the numerator.
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.