The Jeans equations are analogous to the Euler equations for fluid flow and may be derived from the collisionless Boltzmann equation.
32.
The perturbed pressures are evaluated in terms of streamfunctions, using the horizontal momentum equation of the linearised Euler equations for the perturbations,
33.
Inviscid flow is governed by the Euler equations for which there are many simple solution methods depending on what specific assumptions can be made.
34.
This scheme also provides good results when applied to sets of equations-see results below for this scheme applied to the Euler equations.
35.
In Newton Euler equations, " translational acceleration " is used to mean the instantaneous acceleration of the centre of mass of a body.
36.
The nonlinearity of the convection term is the main problem in solving a stationary or nonstationary Navier-Stokes equation or Euler equation problems.
37.
Note that, with the opposite sign convention, this is the potential generated by a pointlike Euler equations in two-dimensional incompressible flow.
38.
Attempts to construct inviscid steady flow solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.
39.
The Euler equations were extended to incorporate the effects of viscosity in the first half of the 1800s, resulting in the Navier-Stokes equations.
40.
To balance the object in static equilibrium, the following Newton-Euler equations must be met on f _ 1, \ ldots, f _ N:
