wrote in message
oups.com...
Need some help... I have been perpetually confused by the concept of
degrees of freedom and the best way to explain it. Perhaps I am not
alone. I've searched for decent explanations but have never found one
that worked. Given that "n-1" and other degrees of freedom references
appears everywhere...I know I need to find an acceptable explanation of
how and why it's important. Taking it as a given just doesn't cut it.
Would appreciate some input. Thanks

The other responses are mathematical, but perhaps you are seeking a physical
explanation. If so, ask in sci.physics. Cross-posted their for convenience.

Anyway, I consider degrees of freedom as number of independent coordinates
or variables. In other words, how many real variables do you need to
completely describe the configuration of a mechanical system.

Examples: An old-fashioned swing has one degree of freedom (provided you
only swing back and forth). A yo-yo bouncing up and down has one degree of
freedom. A single atom flying around in space has three degrees of freedom
(x, y, and z coordinate). Two atoms flying around independently have a total
of six degrees of freedom, three each. Two atoms connected together such
that their mutual distance is constant have five degrees of freedom (three
to specify one atom, and two to specify the relative position of the other
atom).

In thermodynamical equilibrium, each degree of freedom has the same amount
of energy. Temperature essentially measures the average amount of energy per
degree of freedom.

Hope some of that helped.

-Michael.