Hi folks

Is anyone able to put the word holonomic into plain language please. It is defined here:

http://en.wikipedia.org/wiki/Holonomic

I have no idea what this sentence means:

A holonomic basis for a manifold is a set of basis vectors ek for which all Lie derivatives vanish.

That would be great and would help me a lot!

Cheers 🙂

A holonomic basis for a manifold is a set of basis vectors ek for which all Lie derivatives vanish.

😯 say what now

When you start looking at the links and you end up with phrases like “Note: the Einstein summation convention of summing on repeated indices is used below.” it’s probably time to start running 🙂

I think the manifold is part of car engine, if that’s any help.

I’ve only come acroos the term in reference to theories of non-localised memory function in the brain.

Benn a while since I read any of that stuff, only thing I can remember right now is Dr Karl Pribram’s holonomic brain theory and it’s ideas that wave interference phenomena produced perception of objects in the brain.
This (somehow) related to a model for the non-locality of memory storage.
One of the major concepts in this model was that mind is an extension of (a) singularity – I didn’t quite “get” it but found it fascinating nontheless…..

….probabaly not what you were looking for 😕

I think the manifold is part of car engine, if that’s any help.

Sounds about right, I read that description and it left me exhausted.

something about the exhaust manifold on a Vauxhall Vectra?

maybe worth considering what isn’t a holonomic system:

http://en.wikipedia.org/wiki/Non-holonomic_system

wiki: A nonholonomic system in physics and mathematics is a system whose state depends on the path taken to achieve it. Such a system is described by a set of parameters subject to differential constraints, such that when the system evolves along a path in its parameter space (the parameters varying continuously in values) but finally returns to the original set of values at the start of the path, the system itself may not have returned to its original state.

More precisely, a nonholonomic system, also called an anholonomic system, is one in which there is a continuous closed circuit of the governing parameters, by which the system may be transformed from any given state to any other state

Note the examples given, a simple pedulum versus the Foucault pendulum.

I tend to think of them as static vs. dynamic systems, which isn’t quite correct, but all my brain can cope with. I’m sure I’ve read a more concise explantion somewhere, but my physics textbooks are at home.

Cheers folks.

i am writing a piece on the holons, and wanted to have short piece looking at the different uses of this word in different disciplines, but I may have to rethink this!

This is Hollowgnomic object if it helps.

I’m unsure if, when lie derivatives vanish, it means something special, or whether it means the lie derivatives are equal to zero.

If the latter, imagine you have a curved surface with water flowing across it. You know the velocity of water at every point on this surface. You want this velocity to be zero, everwhere. The velocity you have to add, or take away, to make it zero, at every point, is your ‘holomic basis’ or ‘basis vector’ for your curved surface (or ‘manifold’).

Maybe. Treat me as a bloke down the pub.

http://mathworld.wolfram.com/HolonomicFunction.html

Holonomic Function

A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.