When two or more normal vibrations have the same symmetry a full normal coordinate analysis must be performed ( see GF method ).
12.
Given by any orthonormal, and the resulting coordinate system is then known as a "'Riemannian normal coordinate system " '.
13.
These pressures are visually fed back to the patient via a monitor who can regain the normal coordinated movement of the muscles after a few sessions.
14.
This gives rise to the additional normal coordinates, which, as the form of the Hamiltonian indicates, we may view as independent species of phonons.
15.
This idea was implemented in a fundamental way by Albert Einstein in the general theory of relativity : the equivalence principle uses normal coordinates via inertial frames.
16.
In the following, assume that U is a normal neighborhood centered at a point p in M and x ^ i are normal coordinates on U.
17.
Each normal coordinate " U k " represents an independent vibrational mode of the lattice with wavenumber " k " which is known as a normal mode.
18.
The " equatorial " system is the normal coordinate system for most professional and many amateur astronomers having an equatorial mount that follows the movement of the sky during the night.
19.
For this property, one can use a normal coordinate system, which also allows one to show that the topology induced by " d " is the same as the original topology on " M ".
20.
Interesting new phenomena occur; owing to the equivalence principle the quantization procedure locally resembles that of normal coordinates where the affine connection at the origin is set to zero and a nonzero Riemann tensor in general once the proper ( curvature ), can the notion of incoming and outgoing particle be recovered, thus enabling one to define an S-matrix.
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