Holonomic (introduced by
Heinrich Hertz
Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electrom ...
in 1894 from the Greek ὅλος meaning whole, entire and νόμ-ος meaning law)
may refer to:
Mathematics
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Holonomic basis In mathematics and mathematical physics, a coordinate basis or holonomic basis for a differentiable manifold is a set of basis vector fields defined at every point of a region of the manifold as
:\mathbf_ = \lim_ \frac ,
where is the displace ...
, a set of basis vector fields such that some coordinate system exists for which
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Holonomic constraints
In classical mechanics, holonomic constraints are relations between the position variables (and possibly time) that can be expressed in the following form:
:f(u_1, u_2, u_3,\ldots, u_n, t) = 0
where \ are the ''n'' generalized coordinates that d ...
, which are expressible as a function of the coordinates
and time
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Holonomic module
In mathematics, a ''D''-module is a module over a ring ''D'' of differential operators. The major interest of such ''D''-modules is as an approach to the theory of linear partial differential equations. Since around 1970, ''D''-module theory has be ...
in the theory of D-modules
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Holonomic function
In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable d ...
, a smooth function that is a solution of a linear homogeneous differential equation with polynomial coefficients
Other uses
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Holonomic brain theory
Holonomic brain theory, also known as The Holographic Brain, is a branch of neuroscience investigating the idea that human consciousness is formed by quantum effects in or between brain cells. Holonomic refers to representations in a Hilbert phas ...
, model of cognitive function as being guided by a matrix of neurological wave interference patterns
See also
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Holonomy
In differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus ...
in differential geometry
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Holon (disambiguation)
Holon is a city on the central coastal strip south of Tel Aviv, Israel.
Holon may also refer to:
* ''Holon'' (Nik Bärtsch album), 2008
* ''Holon'' (Equinox album), 1998
* Holon (philosophy), something that is simultaneously a whole and a par ...
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Nonholonomic system
A nonholonomic system in physics and mathematics is a physical system whose state depends on the path taken in order to achieve it. Such a system is described by a set of parameters subject to differential constraints and non-linear constraints, s ...
, in physics, a system whose state depends on the path taken in order to achieve it
References
{{mathematical disambiguation