Newtonian Dynamics - Internal Presentation of The Velocity Vector

Internal Presentation of The Velocity Vector

The velocity vector of the constrained Newtonian dynamical system is expressed in terms of the partial derivatives of the vector-function (7):

\displaystyle\mathbf v=\sum^n_{i=1}\frac{\partial\mathbf r}{\partial q^i}\,\dot q^i .

(8)

The quantities are called internal components of the velocity vector. Sometimes they are denoted with the use of a separate symbol

\displaystyle\dot q^i=w^i,\qquad i=1,\,\ldots,\,n

(9)

and then treated as independent variables. The quantities

\displaystyle q^1,\,\ldots,\,q^n,\,w^1,\,\ldots,\,w^n

(10)

are used as internal coordinates of a point of the phase space of the constrained Newtonian dynamical system.

Read more about this topic:  Newtonian Dynamics

Famous quotes containing the words internal and/or presentation:

    “When a person doesn’t understand something, he feels internal discord: however he doesn’t search for that discord in himself, as he should, but searches outside of himself. Thence a war develops with that which he doesn’t understand.”
    —Anton Pavlovich Chekhov (1860–1904)

    “He uses his folly like a stalking-horse, and under the presentation of that he shoots his wit.”
    —William Shakespeare (1564–1616)