CATEGORII DOCUMENTE |

Bulgara | Ceha slovaca | Croata | Engleza | Estona | Finlandeza | Franceza |

Germana | Italiana | Letona | Lituaniana | Maghiara | Olandeza | Poloneza |

Sarba | Slovena | Spaniola | Suedeza | Turca | Ucraineana |

+ Font mai mare | - Font mai mic

The scalar product of two vectors

_{}** and _{} is a scalar.**

**Its value is:**

_{} ** **

_{}** _{}.**

The scalar product is commutative:

_{} **(1.3) _{}**

The vectorial
product of two vectors _{}and _{}is a
vector perpendicular on the plane determined by those vectors, directed in such
a manner that the trihedral _{} _{}and _{}should be
rectangular.

_{} ** **

The modulus of the vectorial product is given by the relation:

_{} ** **

The vectorial product is non-commutative:

_{} ** **

**The mixed product**** of
three vectors _{},_{} and _{} is a scalar.**

_{} ** **

**The double vectorial product** **of three vectors _{},_{} and _{} is a vector situated in the plane _{}.**

The formula of the double vectorial product:

_{} ** **

The operator
_{}is defined
by:

_{} ** **

_{}** applied to a scalar is called gradient. _{}**

_{}** (1.10)**

_{}** scalary applied to a vector is called
divarication. _{}**

_{}** (1.11)**

_{}** vectorially applied to a vector is called
rotor. _{} **

_{} ** **

**Operations
with _{}: **

_{}** (1.13)**

_{}** (1.14)**

_{}** (1.15)**

When _{} acts upon a
product:

**in the first place has differential and only
then vectorial proprieties;**

**all the vectors or the scalars upon which it
doesnt act must, in the end, be placed in front of the operator;**

**it mustnt be placed alone at the end.**

_{}** (1.16)**

_{}** (1.17)**

_{}** (1.18)**

_{}** (1.19)**

_{}** (1.20)**

_{}** (1.21)**

_{}** (1.22)**

_{}** (1.23)**

_{}** ****the scalar _{} considered constant,**

_{}**-
the scalar _{} considered constant,**

_{}**-
the vector _{} considered
constant,**

_{}**-
the vector _{} considered
constant.**

**If:**

_{}** (1.24)**

**then:**

_{}** (1.25)**

**The
streamline is a curve tangent in each of its points to the velocity vector of
the corresponding point _{}.**

**The
equation of the streamline is obtained by writing that the tangent to
streamline is parallel to the vector velocity in its corresponding point:**

_{}** (1.26)**

**The
whirl line is a curve tangent in each of its points to the whirl vector of the
corresponding point _{}.**

_{}** (1.27)**

**The
equation of the whirl line is obtained by writing that the tangent to whirl
line is parallel with the vector whirl in its corresponding point:**

_{}** (1.28)**

**Gauss-Ostrogradskis
relation:**

_{}** (1.29)**

**where
_{}-
volume delimited by surface _{}.**

**The
circulation of velocity on a curve (C) is defined by: **

_{}** (1.30)**

**in
which**

_{}** (1.31)**

**represents
the orientated element of the curve ( _{}- the versor
of the tangent to the curve (C )).**

** **

Fig.1.1

_{}** (1.32)**

The sense of circulation depends on the admitted sense in covering the curve.

_{}** (1.33)**

**Also:**

_{}** (1.34)**

**Stokes
relation:**

_{}** (1.35)**

**in
which _{} represents the versor of the normal to the
arbitrary surface _{} bordered by the curve (C).**

Politica de confidentialitate | Termeni si conditii de utilizare |

Vizualizari: 981

Importanta:

Termeni si conditii de utilizare | Contact

© SCRIGROUP 2024 . All rights reserved