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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.
This reduces the parametric equations of motion of the particle to a Cartesian relationship of speed versus position. This relation is useful when time is unknown. We also know that = or is the area under a velocity–time graph. [15] Velocity Time physics graph
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 = = =.
In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity.
which is a Bernoulli equation valid also for unsteady—or time dependent—flows. Here ∂φ / ∂t denotes the partial derivative of the velocity potential φ with respect to time t, and v = | ∇φ | is the flow speed. The function f(t) depends only on time and not on position in the fluid.
If the kinetic energy is a homogeneous function of degree 2 of the generalized velocities, and the Lagrangian is explicitly time-independent, then: ((˙), (˙ ˙),) = ((˙), ˙ ˙,), (, ˙), where λ is a constant, then the Hamiltonian will be the total conserved energy, equal to the total kinetic and potential energies of the system: = + =.
The kinematics equations of serial and parallel robots can be viewed as relating parameters, such as joint angles, that are under the control of actuators to the position and orientation [T] of the end-effector. From this point of view the kinematics equations can be used in two different ways.
The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; [2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction of ...