Search results
Results from the WOW.Com Content Network
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 = = =.
By the fundamental theorem of calculus, it can be seen that the integral of the acceleration function a(t) is the velocity function v(t); that is, the area under the curve of an acceleration vs. time (a vs. t) graph corresponds to the change of velocity. =.
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 green line shows the slope of the velocity-time graph at the particular point where the two lines touch. Its slope is the acceleration at that point. In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object.
An elastically deformable mass deforms under an applied force (or acceleration); the deformation is a function of its stiffness and the magnitude of the force. If the change in force is slow, the jerk is small, and the propagation of deformation is considered instantaneous as compared to the change in acceleration.
Note in the graphs that L is rod length and R is half stroke . The vertical axis units are inches for position, [inches/rad] for velocity, [inches/rad²] for acceleration. The horizontal axis units are crank angle degrees.
These relationships can be demonstrated graphically. The gradient of a line on a displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under a graph of acceleration versus time is equal to the change in velocity.
The concept of acceleration is a covariant derivative concept. In other words, in order to define acceleration an additional structure on M {\displaystyle M} must be given. Using abstract index notation , the acceleration of a given curve with unit tangent vector ξ a {\displaystyle \xi ^{a}} is given by ξ b ∇ b ξ a {\displaystyle \xi ^{b ...