Vector Identities
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Algebraic vector relations:
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| 7. | whereas nˆ _| E→ and nˆ _| B→ | |
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Differential vector relations:
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Integral vector relations:
| 48. | whereas ƒ denotes a spatial scalar function, V is volume and S is surface | |
| 49. | Gauss[1]-Ostrogradsky[2] theorem, 3D continuum theorem | |
| 50. | Stokes[3] theorem, whereas E→ denotes spatial vector function | |
| 51. | Green[4] theorem | |
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Vector relations between space and time:
| 57. | Angular velocity of the radius vector | |
| 58. | Angular velocity of the velocity vector and this is usual mechanical meaning of angular velocity | |
| 59. | Angular velocity of the velocity vector rotation in persistent space, this is valid in persistent space only | |
| 60. | Connection between velocity, angular velocity and radius of the curve | |
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| 62. | Inverse radius of the curve which matches vector of rotation | |
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| 64. | 3D continuum equation, whereas v→ is speed of field's displacement and n is spatial density in persistent space | |
| 65. | 2D continuum equation, whereas v→ is speed of field's displacement, n→ is area density of lines that pervades generalized surface in persistent space | |
| 66. | Time derivation of magnitude of arbitrary vector E→ | |
| 67. | Time derivation of ort vector of an arbitrary vector E→ |
DESCARTES COORDINATE SYSTEM:
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CYLINDRICAL COORDINATE SYSTEM:
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SPHERICAL COORDINATE SYSTEM:
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References:
[1] Johann Carl Friedrich Gauss (Gauß), 1777 – 1855
[2] Mikhail Ostrogradsky, 1801 – 1862
[3] George Gabriel Stokes, 1819 – 1903
[4] George Green, 1793 – 1841
Owner of the patent
Dipl.El.-Ing. Andrija Radović
E-mails: andrijar@gmail.com, andrijaradovic@hotmail.com or andrijar@andrijar.com.
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