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:

    “I maintain that I have been a Negro three times—a Negro baby, a Negro girl and a Negro woman. Still, if you have received no clear cut impression of what the Negro in America is like, then you are in the same place with me. There is no The Negro here. Our lives are so diversified, internal attitudes so varied, appearances and capabilities so different, that there is no possible classification so catholic that it will cover us all, except My people! My people!”
    —Zora Neale Hurston (1891–1960)

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