Friday, 20 April 2018

Obi Theory Birth Again for PONTLYAGIN L. S.

1
Obi’s birth of whirl starts at energy’s unbalance existence in universe.
2
 Now define vector field of smooth curved surface M.
Here touch plane of M is expressed by TxM.
Vector field is expressed by the following differential equation’s solution curve.
x(t) is contained in M
d/dt x(t)  is contained in Tx(t)M
3
Now define torus’ surface.
Here x is on surface M.
α limit set of x is expressed by α(x).
Now set a point (θ12on M.
When differential equation system on M that becomes torus and the solution is expressed by double cycleα(x) becomes all torus’ surface.
4
Now express obi.
Obi’s solution curb is expressed by polar coordinates (ρ, θ).
ρ = k exp(α/β  θ)    α is contained in eαt, β is angular velocity, k is consonant
Obi is logarithmic helix.
5
Here suppose torus as obi’s differential-like figure.
For obi’s instantaneous figure, torus is examined by analytic geometry.
6
Obi’s whirl is also examined from torus’ movement  as obi’s instantaneous figure.
7
Obi’s birth is also examined from torus as obi figure’s origin.

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