GENERAL VECTOR IDENTITIES, selection by Andrija Radović

Algebraic vector relations:

1.                                   Whereas  and .
2.

Differential vector relations:

3.

Integral vector relations:

4.                                     ƒ denotes a spatial scalar function, V is volume and S is surface.
5.                                   Gauss[1]-Ostrogradsky[2] theorem, 3D continuum theorem.
6.                           Stokes[3] theorem, whereas  denotes spatial vector function.
7.                                   Green[4] theorem.
8.

Vector relations between space and time:

9.                                          Angular velocity of the radius vector.
10.                                    Angular velocity of the velocity vector and this is usual mechanical meaning of angular velocity.
11.                                                       Angular velocity of the velocity vector rotation in persistent space, this is valid in persistent space only.
12.                                                        Connection between velocity, angular velocity and radius of the curve.
13.                    Inverse radius of the curve which matches vector of rotation.
14.                                                 3D continuum equation, whereas  is speed of field's displacement and n is spatial density in persistent space.
15.                                             2D continuum equation, whereas  is speed of field's displacement,  is area density of lines that pervades generalized surface in persistent space.
16.                                                  Time derivation of magnitude of arbitrary vector .
17.                       Time derivation of ort vector of an arbitrary vector .

[1] Johann Carl Friedrich Gauss (Gauß), 1777 – 1855

[2] Mikhail Ostrogradsky, 1801 – 1862

[3] George Gabriel Stokes, 1819 – 1903

[4] George Green, 1793 – 1841