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Motion graphs and derivatives. 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. In the International System of Units, the ...
Piston motion equations. The reciprocating motion of a non-offset piston connected to a rotating crank through a connecting rod (as would be found in internal combustion engines) can be expressed by equations of motion. This article shows how these equations of motion can be derived using calculus as functions of angle (angle domain) and 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.
A slider-crank linkage is a four-link mechanism with three revolute joints and one prismatic (sliding) joint. [1] The rotation of the crank drives the linear movement of the slider, or the expansion of gases against a sliding piston in a cylinder can drive the rotation of the crank. There are two types of slider-cranks: in-line and offset.
(the apparent motion of the wave due to the successive oscillations of particles or fields about their equilibrium positions) propagates at the phase and group velocities parallel or antiparallel to the propagation direction, which is common to longitudinal and transverse waves.
A motion chart is a dynamic bubble chart which allows efficient and interactive exploration and visualization of longitudinal multivariate data. [1] Motion charts provide mechanisms for mapping ordinal, nominal and quantitative variables onto time, 2D coordinate axes, size, colors, glyphs and appearance characteristics, which facilitate the ...
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [1]
Screw theory. Screw theory is the algebraic calculation of pairs of vectors, such as angular and linear velocity, or forces and moments, that arise in the kinematics and dynamics of rigid bodies. [1][2] Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw ...