GENERAL VECTOR IDENTITIES, selection by Andrija Radović

- Whereas
^{}and^{}. - ƒ denotes a spatial scalar function, V is volume and S is surface.
- Gauss[1]-Ostrogradsky[2] theorem, 3D continuum theorem.
- Stokes[3] theorem, whereas
^{}denotes spatial vector function. - Green[4] theorem.
- Angular velocity of the radius vector.
- Angular velocity of the velocity vector and this is usual mechanical meaning of angular velocity.
- Angular velocity of the velocity vector rotation in persistent space, this is valid in persistent space only.
- Connection between velocity, angular velocity and radius of the curve.
- Inverse radius of the curve which matches vector of rotation.
- 3D continuum equation, whereas
^{}is speed of field's displacement and n is spatial density in persistent space. - 2D continuum equation, whereas
^{}is speed of field's displacement,^{}is area density of lines that pervades generalized surface in persistent space. - Time derivation of magnitude of arbitrary vector
^{}. - Time derivation of ort vector of an arbitrary vector
^{}.

Algebraic vector relations:

Differential vector relations:

Integral vector relations:

Vector relations between space and time:

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

[2] Mikhail Ostrogradsky, 1801 – 1862

[3] George Gabriel Stokes, 1819 – 1903

[4] George Green, 1793 – 1841

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