## momenta

mo·men·tanoun

A plural of momentum

## momenta

Noun

- plural form of
*momentum*

- If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and
**momenta**can be found from the Hamiltonian equations aE aE qr = 49 - 1 57., gr where q r denotes dg r ldt, &c., and E is the total energy expressed as a function of pi, qi,. - Thus after a time dt the values of the coordinates and
**momenta**of the small group of systems under consideration will lie within a range such that pi is between pi +pidt and pi +dp,+(pi+ap?dpi) dt „ qi +gidt „ qi+dqi+ (qi +agLdgi) dt, Thus the extension of the range after the interval dt is dp i (i +aidt) dq i (I +?gidt). - Since the values of the co-ordinates and
**momenta**at any instant during the motion may be treated as " initial " values, it is clear that the " extension " of the range must remain constant throughout the whole motion. - This result at once disposes of the possibility of all the systems acquiring any common characteristic in the course of their motion through a tendency for their co-ordinates or
**momenta**to concentrate about any particular set, or series of sets, of values. - Let us imagine that the systems had the initial values of their co-ordinates and
**momenta**so arranged that the number of systems for which the co-ordinates and**momenta**were within a given range was proportional simply to the extension of the range.

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