Pathways Through Applied and Computational Physics by Nicolò Barbero Matteo Delfino Carlo Palmisano & Gianfranco Zosi

Author:Nicolò Barbero, Matteo Delfino, Carlo Palmisano & Gianfranco Zosi
Language: eng
Format: epub
Publisher: Springer Milan, Milano

Then, an equation of the form

(3.2.11)

describes the path of a particle located at X when t=t 0.

If we let X=X 1 e 1+X 2 e 2+X 3 e 3 and x=x 1 e 1+x 2 e 2+x 3 e 3, Eq. (3.2.11) takes the component form

(3.2.12)

or, equivalently,

(3.2.13)

In Eq. (3.2.12) the triplet X 1,X 2,X 3 identifies the material coordinates of the different particles of the body at t 0 and Eq. (3.2.11) defines the trajectory of a given particle as times flows. Obviously, the individual particles of a body cannot execute arbitrary motions independently of one another. In particular, it seems realistic to predict that two different particles will not end up in the same place. For these reasons, we assume that the mapping in Eq. (3.2.11) is one-to-one, i.e., the functions are single-valued, continuous and with a unique inverse

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