In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x:
In mechanics and physics, simple harmonic motion is a special type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position. It results in an oscillation which continues indefinitely, if uninhibited by friction or any other dissipation of energy.
In physics, the Navier–Stokes equations are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency.
In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important. Its magnitude is either the wavenumber or angular wavenumber of the wave, and its direction is ordinarily the direction of wave propagation.
In physics, the Polyakov action is an action of the two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was introduced by Stanley Deser and Bruno Zumino and independently by L. Brink, P. Di Vecchia and P. S. Howe in 1976, and has become associated with Alexander Polyakov after he made use of it in quantizing the string in 1981. The action reads
In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, relative to viscous forces.
In fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen.
In relativistic physics, the Born coordinate chart is a coordinate chart for Minkowski spacetime, the flat spacetime of special relativity. It is often used to analyze the physical experience of observers who ride on a ring or disk rigidly rotating at relativistic speeds, so called Langevin observers. This chart is often attributed to Max Born, due to his 1909 work on the relativistic physics of a rotating body. For overview of the application of accelerations in flat spacetime, see Acceleration and proper reference frame.
The Womersley number is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects. It is named after John R. Womersley (1907–1958) for his work with blood flow in arteries. The Womersley number is important in keeping dynamic similarity when scaling an experiment. An example of this is scaling up the vascular system for experimental study. The Womersley number is also important in determining the thickness of the boundary layer to see if entrance effects can be ignored.
The Mathieu equation is a linear second-order differential equation with periodic coefficients. The French mathematician, E. Léonard Mathieu, first introduced this family of differential equations, nowadays termed Mathieu equations, in his “Memoir on vibrations of an elliptic membrane” in 1868. "Mathieu functions are applicable to a wide variety of physical phenomena, e.g., diffraction, amplitude distortion, inverted pendulum, stability of a floating body, radio frequency quadrupole, and vibration in a medium with modulated density"
In general relativity, Lense–Thirring precession or the Lense–Thirring effect is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth. It is a gravitomagnetic frame-dragging effect. It is a prediction of general relativity consisting of secular precessions of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with angular momentum .
A Taylor column is a fluid dynamics phenomenon that occurs as a result of the Coriolis effect. It was named after Geoffrey Ingram Taylor. Rotating fluids that are perturbed by a solid body tend to form columns parallel to the axis of rotation called Taylor columns.
The Taylor microscale, which is sometimes called the turbulence length scale, is a length scale used to characterize a turbulent fluid flow. This microscale is named after Geoffrey Ingram Taylor. The Taylor microscale is the intermediate length scale at which fluid viscosity significantly affects the dynamics of turbulent eddies in the flow. This length scale is traditionally applied to turbulent flow which can be characterized by a Kolmogorov spectrum of velocity fluctuations. In such a flow, length scales which are larger than the Taylor microscale are not strongly affected by viscosity. These larger length scales in the flow are generally referred to as the inertial range. Below the Taylor microscale the turbulent motions are subject to strong viscous forces and kinetic energy is dissipated into heat. These shorter length scale motions are generally termed the dissipation range.
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels with the same boundary conditions and the same Reynolds and Womersley numbers, then the fluid flows will be identical. This can be seen from inspection of the underlying Navier-Stokes equation, with geometrically similar bodies, equal Reynolds and Womersley Numbers the functions of velocity (u’,v’,w’) and pressure (P’) for any variation of flow.
Kapitza's pendulum or Kapitza pendulum is a rigid pendulum in which the pivot point vibrates in a vertical direction, up and down. It is named after Russian Nobel laureate physicist Pyotr Kapitza, who in 1951 developed a theory which successfully explains some of its unusual properties. The unique feature of the Kapitza pendulum is that the vibrating suspension can cause it to balance stably in an inverted position, with the bob above the suspension point. In the usual pendulum with a fixed suspension, the only stable equilibrium position is with the bob hanging below the suspension point; the inverted position is a point of unstable equilibrium, and the smallest perturbation moves the pendulum out of equilibrium. In nonlinear control theory the Kapitza pendulum is used as an example of a parametric oscillator that demonstrates the concept of "dynamic stabilization".
Von Kármán swirling flow is a flow created by a uniformly rotating infinitely long plane disk, named after Theodore von Kármán who solved the problem in 1921. The rotating disk acts as a fluid pump and is used as a model for centrifugal fans or compressors. This flow is classified under the category of steady flows in which vorticity generated at a solid surface is prevented from diffusing far away by an opposing convection, the other examples being the Blasius boundary layer with suction, stagnation point flow etc.
In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problem that have exact solution for the Navier-Stokes equations. The impulse movement of semi-infinite plate was studied by Keith Stewartson.
In fluid dynamics, Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer is a problem of determining the flow created by an oscillating solid surface, named after Sir George Stokes. This is considered one of the simplest unsteady problem that have exact solution for the Navier-Stokes equations. In turbulent flow, this is still named a Stokes boundary layer, but now one has to rely on experiments, numerical simulations or approximate methods in order to obtain useful information on the flow.
In fluid dynamics, Beltrami flows are flows in which the vorticity vector and the velocity vector are parallel to each other. In other words, Beltrami flow is a flow where Lamb vector is zero. It is named after the Italian mathematician Eugenio Beltrami due to his derivation of the Beltrami vector field, while initial developments in fluid dynamics were done by the Russian scientist Ippolit S. Gromeka in 1881.
