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Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). [2] This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume.
A solid is a material that can support a substantial amount of shearing force over a given time scale during a natural or industrial process or action. This is what distinguishes solids from fluids, because fluids also support normal forces which are those forces that are directed perpendicular to the material plane across from which they act and normal stress is the normal force per unit area ...
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 red particle moves in a flowing fluid; its pathline is traced in red; the tip of the trail of blue ink released from the origin follows the particle, but unlike the static pathline (which records the earlier motion of the dot), ink released after the red dot departs continues to move up with the flow.
In the tautochrone problem, if the particle's position is parametrized by the arclength s(t) from the lowest point, the kinetic energy is then proportional to ˙, and the potential energy is proportional to the height h(s). One way the curve in the tautochrone problem can be an isochrone is if the Lagrangian is mathematically equivalent to a ...
In general, the term motion signifies a continuous change in the position or configuration of a physical system in space. For example, one can talk about the motion of a wave or the motion of a quantum particle, where the configuration consists of the probabilities of the wave or particle occupying specific positions.
Momentum space is the set of all momentum vectors p a physical system can have; the momentum vector of a particle corresponds to its motion, with dimension of mass ⋅ length ⋅ time −1. Mathematically, the duality between position and momentum is an example of Pontryagin duality .
The definition above relied on the physical nature of a fluid current; however, no laws of physics were invoked (for example, it was assumed that a lightweight particle in a river will follow the velocity of the water), but it turns out that many physical concepts can be described concisely using the material derivative.
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