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In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
For < <, (= represents solid body rotation, the whole fluid rotates at the same speed) the solution reaches the solid body rotation at infinity in an oscillating manner from the plate. The axial velocity is negative w < 0 {\displaystyle w<0} for 0 ≤ γ < 1 {\displaystyle 0\leq \gamma <1} and positive w > 0 {\displaystyle w>0} for 1 < γ < ∞ ...
In fluid dynamics, the Kirchhoff equations, named after Gustav Kirchhoff, describe the motion of a rigid body in an ideal fluid. = + + +, = + +, = (~ +) = ^, = ^ where and are the angular and linear velocity vectors at the point , respectively; ~ is the moment of inertia tensor, is the body's mass; ^ is a unit normal vector to the surface of the body at the point ; is a pressure at this point ...
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.
For constant fluid density, the incompressible equations can be written as a quasilinear advection equation for the fluid velocity together with an elliptic Poisson's equation for the pressure. On the other hand, the compressible Euler equations form a quasilinear hyperbolic system of conservation equations .
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Vortex – Fluid flow revolving around an axis of rotation; Water hammer – Pressure surge when a fluid is forced to stop or change direction suddenly; Wave drag – Aircraft aerodynamic drag at transonic and supersonic speeds due to the presence of shock waves; Wind – Natural movement of air or other gases relative to a planet's surface