Search results
Results from the WOW.Com Content Network
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 original Langevin equation [1] [2] describes Brownian motion, the apparently random movement of a particle in a fluid due to collisions with the molecules of the fluid, = + (). Here, v {\displaystyle \mathbf {v} } is the velocity of the particle, λ {\displaystyle \lambda } is its damping coefficient, and m {\displaystyle m} is its mass.
The solution of these equations also reveals the precise form of the particle motion, which equations (1) and (2) represent in generic form only. It is found that equation (3) gives rise to a family of waves whose motion is symmetrical about the midplane of the plate (the plane z = 0), while equation (4) gives rise to a family of waves whose ...
In the case of a large , the value of is small if the masses are approximately the same: hitting a much lighter particle does not change the velocity much, hitting a much heavier particle causes the fast particle to bounce back with high speed.
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan [2] and Lucy [3] in 1977, initially for astrophysical problems.
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
The complete two-body problem can be solved by re-formulating it as two one-body problems: a trivial one and one that involves solving for the motion of one particle in an external potential. Since many one-body problems can be solved exactly, the corresponding two-body problem can also be solved.
The fundamental assumption of the method is that the material consists of separate, discrete particles. These particles may have different shapes and properties that influence inter-particle contact. Some examples are: liquids and solutions, for instance of sugar or proteins; bulk materials in storage silos, like cereal; granular matter, like sand;