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searching for Generalized coordinates 30 found (102 total)

Conserved quantity (522 words) [view diff] exact match in snippet view article find links to article

Hamiltonian H {\displaystyle {\mathcal {H}}} , a function f of the generalized coordinates q and generalized momenta p has time evolution d f d t = { f ,

Projective plane (6,933 words) [view diff] no match in snippet view article find links to article

In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect

Rayleigh dissipation function (665 words) [view diff] exact match in snippet view article find links to article

potential. This relationship is represented in terms of the set of generalized coordinates q i = { q 1 , q 2 , … q n } {\displaystyle q_{i}=\left\{q_{1},q_{2}

Multibody system (1,818 words) [view diff] exact match in snippet view article find links to article

coordinates than degrees of freedom of the underlying system. The generalized coordinates are denoted by q {\displaystyle \mathbf {q} } , the mass matrix

Stochastic Eulerian Lagrangian method (1,046 words) [view diff] exact match in snippet view article find links to article

been introduced allowing for descriptions of structures involving generalized coordinates and additional translational or rotational degrees of freedom.

Classical mechanics (5,857 words) [view diff] exact match in snippet view article find links to article

branches of analytical mechanics are Lagrangian mechanics, which uses generalized coordinates and corresponding generalized velocities in tangent bundle space

Electromechanical modeling (387 words) [view diff] exact match in snippet view article find links to article

systems is mainly based on the Lagrangian which is a function of the generalized coordinates and the associated velocities. If all forces are derivable from

Moving frame (2,587 words) [view diff] no match in snippet view article find links to article

automorphisms is G. A smooth manifold Σ which serves as a space of (generalized) coordinates for X. A collection of frames ƒ each of which determines a coordinate

Hamiltonian (quantum mechanics) (5,042 words) [view diff] exact match in snippet view article

Hamilton's equations, with the a n {\displaystyle a_{n}} s as the generalized coordinates, the π n {\displaystyle \pi _{n}} s as the conjugate momenta, and

D'Alembert's principle (2,532 words) [view diff] exact match in snippet view article find links to article

system of n {\displaystyle n} rigid bodies with m {\displaystyle m} generalized coordinates requires δ W = ( Q 1 + Q 1 ∗ ) δ q 1 + ⋯ + ( Q m + Q m ∗ ) δ q

Pfaffian constraint (653 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}} are the n generalized coordinates that describe the system, and where L {\displaystyle L} is the

Stress–energy tensor (4,040 words) [view diff] exact match in snippet view article find links to article

by looking at the total derivative with respect to one of the generalized coordinates of the system. So, with our condition ∂ L ∂ x ν = 0 {\displaystyle

Lagrange bracket (1,009 words) [view diff] exact match in snippet view article find links to article

\eta _{j}]=-\delta _{ij}} Note that the summation here involves generalized coordinates as well as generalized momentum. The invariance of Lagrange bracket

William Elwood Byerly (192 words) [view diff] case mismatch in snippet view article find links to article

Treatise on Fourier's Series (1893) An Introduction to the Use of Generalized Coordinates in Mechanics and Physics (1916) J. L. Coolidge, "William Elwood

Canonical ensemble (2,828 words) [view diff] exact match in snippet view article find links to article

q1, … qn are the canonical coordinates (generalized momenta and generalized coordinates) of the system's internal degrees of freedom. In a system of particles

Poisson bracket (4,029 words) [view diff] exact match in snippet view article find links to article

\eta _{j}]=-\delta _{ij}} Note that the summation here involves generalized coordinates as well as generalized momentum. The invariance of Poisson bracket

Spherical pendulum (1,775 words) [view diff] exact match in snippet view article find links to article

of the Lagrangian L = T − V {\displaystyle L=T-V} in arbitrary generalized coordinates the position of the mass is expressed along Cartesian axes. Here

James John Smith (659 words) [view diff] exact match in snippet view article find links to article

1932 at Zürich with the talk An expression of Green's function in generalized coordinates. "The solution of differential equations by a method similar to

Émilie du Châtelet (6,458 words) [view diff] exact match in snippet view article find links to article

true for all problems where the initial state is symmetric in generalized coordinates. E.g., mechanical energy, either kinetic or potential, may be lost

Grand canonical ensemble (5,285 words) [view diff] exact match in snippet view article find links to article

q1, … qn are the canonical coordinates (generalized momenta and generalized coordinates) of the system's internal degrees of freedom. The expression for

Christoffel symbols (8,323 words) [view diff] exact match in snippet view article find links to article

symbols explicitly appear. Let x i {\displaystyle x^{i}} be the generalized coordinates and x ˙ i {\displaystyle {\dot {x}}^{i}} be the generalized velocities

Inverted pendulum (4,486 words) [view diff] exact match in snippet view article find links to article

}}\cos \theta +{\frac {1}{2}}m\ell ^{2}{\dot {\theta }}^{2}.} The generalized coordinates of the system are θ {\displaystyle \theta } and x {\displaystyle

Perturbation theory (quantum mechanics) (15,991 words) [view diff] exact match in snippet view article

})=H(0)+x^{\mu }F_{\mu }.} If the parameters x μ are considered as generalized coordinates, then Fμ should be identified as the generalized force operators

Barycentric coordinate system (8,177 words) [view diff] exact match in snippet view article find links to article

the case of a simplex, the points with nonnegative normalized generalized coordinates ( 0 ≤ λ i ≤ 1 {\displaystyle 0\leq \lambda _{i}\leq 1} ) form the

Lectures on Theoretical Physics (3,068 words) [view diff] case mismatch in snippet view article find links to article

Variational Principles of Mechanics and Lagrange's Equations For Generalized Coordinates Mechanics of deformable bodies, the second volume of the series

First-class constraint (4,561 words) [view diff] exact match in snippet view article find links to article

are several ways to implement a constraint: one can switch to generalized coordinates that manifestly solve the constraint, or one can use a Lagrange

Rotordynamics (2,260 words) [view diff] exact match in snippet view article find links to article

deflection for inclusion of e.g., centrifugal elements; q(t) is the generalized coordinates of the rotor in inertial coordinates; f(t) is a forcing function

NASA Advanced Supercomputing Division (2,406 words) [view diff] exact match in snippet view article find links to article

incompressible Navier-Stokes equations in two- and three-dimensional generalized coordinates, respectively, for steady-state and time varying flow. In 1994

List of Italian inventions and discoveries (26,253 words) [view diff] exact match in snippet view article find links to article

is known as Lagrangian mechanics, introducing the concepts of generalized coordinates, potential (i.e. gravitational or electrical field) and Lagrangian

Quantum mechanics of nuclear magnetic resonance spectroscopy (836 words) [view diff] exact match in snippet view article find links to article

Hamiltonian H(q, p) is expressed as: H(q, p) = T(p) + V(q) where: q : Generalized coordinates (position variables). p : Generalized momenta (momentum variables)