Thursday, January 19, 2006

GEOMETRIC INTERPRETATION OF ΨΔΨ*

Lets take an area like this:


If we take a volume in an after time, we have:




The volume relative change is:







Now, in 3D, we have that:








The dilatation of volume can be directly relationed with the spacial structure of velocity gradient.





A unit of volume can be TRANSLATED:














Be DEFORMED:


















ROTATED





Or have cutting efforts:

























And







Thus:













This is the angular velocity in Z axis. We can see that when there's a minus sign, it means angular velocity. Same way, we can demostrate that the rest of the two angles is an effort, it means that the formula between parenthesis has a "+" sign.





But, what represents it in Schrödinger's formula?

Answers, next day...

R. Aparicio.

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References:

- Quaternion and Rotation Sequences, Jack B. Kuipers

- Vectors, tensors and the Basic Equations of Fluid Mechanics, Rutherford Aris.

- Vibraciones y ondas. A. P. French.

- Lectures On Clifford (Geometric) Algebras. Rafal Ablamowicz et. al.

- Mecánica de Fluidos. Victor L. Streeter et. al.

- De Natura Visibilium et Invisibilium. R. Aparicio. Ed. Elaleph.

- Siglo XXI: La física que nos espera. R. Aparicio. Ed. Elaleph.

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