reference state. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes...
28 KB (4,543 words) - 17:53, 19 August 2024
Barycentric coordinate system (redirect from Generalized barycentric coordinates)
point not having unique generalized barycentric coordinates except when P is a simplex. Dual to generalized barycentric coordinates are slack variables,...
44 KB (8,186 words) - 13:06, 4 October 2024
details. As Hamiltonian mechanics are generalized by symplectic geometry and canonical transformations are generalized by contact transformations, so the...
6 KB (872 words) - 00:34, 31 October 2023
Lagrangian mechanics (redirect from Cyclic coordinates)
this vk, the kinetic energy in generalized coordinates depends on the generalized velocities, generalized coordinates, and time if the position vectors...
92 KB (14,503 words) - 13:33, 9 October 2024
the generalized coordinates and velocities (q, q̇) with (q, p); the generalized coordinates and the generalized momenta conjugate to the generalized coordinates:...
40 KB (5,758 words) - 22:46, 21 September 2024
mechanics (particularly Lagrangian mechanics), generalized forces are conjugate to generalized coordinates. They are obtained from the applied forces Fi...
5 KB (820 words) - 05:03, 28 October 2023
Coordinate system (redirect from Coordinates)
Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates. Generalized coordinates are...
19 KB (2,285 words) - 06:01, 4 October 2024
formulated in generalized coordinates of motion. Note that "generalized coordinates of motion" are related to—but distinct from—generalized coordinates as used...
18 KB (2,924 words) - 19:14, 17 January 2024
coordinates, which we denote as w {\displaystyle \mathbf {w} } (the action angles, which are the generalized coordinates) and their new generalized momenta...
9 KB (1,511 words) - 00:00, 25 April 2024
the configuration of a system are called generalized coordinates, and the space defined by these coordinates is called the configuration space of the...
10 KB (1,410 words) - 07:45, 25 November 2023
Frame of reference (redirect from Spacetime coordinates)
perspective, the formulation of many problems in physics employs generalized coordinates, normal modes or eigenvectors, which are only indirectly related...
30 KB (3,456 words) - 08:35, 24 September 2024
Momentum (redirect from Generalized Momentum)
symbol Π. In this mathematical framework, a generalized momentum is associated with the generalized coordinates. Its components are defined as p j = ∂ L...
73 KB (9,782 words) - 13:16, 2 October 2024
mechanics). Since Lagrangian mechanics is based on generalized coordinates, transformations of the coordinates q → Q do not affect the form of Lagrange's equations...
60 KB (10,421 words) - 22:25, 13 September 2024
choice of generalized coordinates. For orthogonal coordinates and Hamiltonians that have no time dependence and are quadratic in the generalized momenta...
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Hamiltonian optics (section Generalized coordinates)
q_{N}{\left(\sigma \right)}\right)} described by N {\displaystyle N} generalized coordinates between two specified states at two specified parameters σA and...
34 KB (6,580 words) - 16:57, 23 September 2023
n } {\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}} are n generalized coordinates that describe the system (in unconstrained configuration space)...
22 KB (4,021 words) - 17:03, 20 August 2024
Virtual work (section Generalized inertia forces)
virtual displacements. This can be generalized to an arbitrary mechanical system defined by the generalized coordinates q i {\displaystyle q_{i}} , i = 1...
45 KB (6,342 words) - 14:22, 20 August 2024
Rigid body dynamics (section Generalized forces)
{q}}}}\right),} is the generalized force acting on this one degree of freedom system. If the mechanical system is defined by m generalized coordinates, qj, j = 1...
42 KB (5,759 words) - 06:54, 7 September 2024
states that the true evolution q(t) of a system described by N generalized coordinates q = (q1, q2, ..., qN) between two specified states q1 = q(t1) and...
16 KB (2,268 words) - 01:32, 8 July 2024
Projective plane (section Generalized coordinates)
(geometric) plane through the origin in the 3-space. This idea can be generalized and made more precise as follows. Let K be any division ring (skewfield)...
51 KB (6,625 words) - 23:21, 9 September 2024
are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient...
55 KB (7,476 words) - 10:18, 6 June 2024
involve the generalized velocities. By defining a normalized distance or metric d s {\displaystyle ds} in the space of generalized coordinates d s 2 = d...
13 KB (1,727 words) - 13:49, 10 October 2024
n-tuple of the generalized momenta. A Legendre transformation is performed to change the variables in the total differential of the generalized coordinate...
16 KB (2,328 words) - 11:39, 16 October 2023
the action-angle coordinates, called the "action" of the generalized coordinate qk, is defined by integrating a single generalized momentum around a...
23 KB (2,998 words) - 13:57, 10 October 2024
explicit variable and the equation of constraints can be described by generalized coordinates. Such constraints are called scleronomic constraints. The opposite...
4 KB (649 words) - 04:44, 22 August 2024
= 1. Taking δθ as the ε parameter and the Cartesian coordinates r as the generalized coordinates q, the corresponding Q variables are given by Q = n ×...
66 KB (10,947 words) - 17:29, 20 September 2024
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}...
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Retrieved 2020-11-09. For a description of generalized coordinates, see Ahmed A. Shabana (2003). "Generalized coordinates and kinematic constraints". Dynamics...
49 KB (5,992 words) - 14:32, 7 October 2024
Spherical coordinate system (redirect from Spherical coordinates)
the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane...
43 KB (6,352 words) - 06:34, 4 October 2024
where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity, that particle...
9 KB (1,042 words) - 11:46, 26 July 2024