Holding on to the beat keeps the music functional, stoking the motion on the dance floor; changing it might provide new pleasures but could also break the music's spell.
The actuator should never be smaller than the motion stoke.
Direct numerical simulation of turbulent flows is based on the "primitive" Navier-Stokes equations of motion.
The horizontal acceleration of the copper sphere relative to the water can be determined by measuring the steady-state velocity of the sphere and applying Stokes' law for motion in a resistive medium.
If we suppress the variables θ, z and θ, φ from the Navier-Stokes equations of motion in cylindrical polar coordinates ((r,theta,z,t)) and spherical polar coordinates ((r,theta,varphi,t)), respectively (see [15]), we obtain Burgers' equation (5.1) in polar coordinates.
As an application of this algorithm, we study the motion of Stokes waves in the presence of viscosity.
A particle equation of motion including Stokes drag, lift, buoyancy and gravitational forces is used for particle trajectory analysis.
A more careful analysis indicates that the force according to Stokes formula [4], governing motion of a solid particle in a gaseous or liquid medium, must be multiplied by a factor 3/2 [7] if a gaseous or liquid particle is moving in a liquid.
This so called Stokes' law was improved in the early 20th Century by several authors, who included diverse approximations to the inertia term neglected by Stokes in the Navier-Stokes equation describing Newtonian fluid motion around the sphere.
For instance, the convection-diffusion and Burgers' equations that represent the transport phenomena, and the highly nonlinear Navier-Stokes' (N-S) equations of motion that describe the motion of fluid flow and represent the conservation of mass, momentum and energy.
