velocity configurations and phenomenological description of the square root of negative i © parker...

8/6/2019 Velocity Configurations and Phenomenological Description of the Square Root of Negative i © Parker Emmerson, M…

http://slidepdf.com/reader/full/velocity-configurations-and-phenomenological-description-of-the-square-root 1/28

"Velocity" Configurations

from and Mathematical,

Phenomenological Description of the -Â

Premise

- Â = - -2 p Sin@bD

4 p q - q2

= -2 p Sin@bD

4 p q - q2

-2 p Sin@bD

4 p q - q2

=2 p Sin@bD

4 p q - q2

- -2 p Sin@bD

4 p q - q2

=

r 1 -HvL2

c2

q

1-HvL2

c2

4 p r - r q

2 p r Sin@bD -2 p Sin@bD

4 p q - q2

-2 p Sin@bD

4 p q - q2

SphericalPlot3DB - -4 p q - q2

2 p Sin@bD , 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

.

-1.0

-0.5

0.0

0.5

.0

Printed by Mathematica for Students



SphericalPlot3DB - -4 p q - q2

2 p Sin@bD , 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <F

2 Velocity Configurations and Phenomenological Descprition of the Square Root of Negative i © Parker Emmerson, May 9, 2011.nb




SphericalPlot3DB - -2 p Sin@bD

4 p q - q2

, 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <F

ComputationalGeometry`Methods`SpatialSearch::spoutbounds :

--

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H8-

3.98196, 17.723<L


-- Message text not found -- H84.1067, 17.7732<L

Velocity Configurations and Phenomenological Descprition of the Square Root of Negative i © Parker Emmerson, May 9, 2011.nb 3




SphericalPlot3DB - -2 p Sin@bD

4 p q - q2

, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

.

-1.0

-0.5

0.0

0.5

.0





SphericalPlot3DB -2 p Sin@bD

4 p q - q2

-2 p Sin@bD

4 p q - q2

, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F





SphericalPlot3DB -2 p Sin@bD

4 p q - q2

-2 p Sin@bD

4 p q - q2

, 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <F


--


H8-

0.224399,-

20.8376<L


-- Message text not found -- H812.5664, 52.7351<L


-- Message text not found -- H8-6.58572, -24.9965<L

General::stop :

Further output of ComputationalGeometry`Methods`SpatialSearch::spoutbounds will be suppressed

during this calculation. à





SphericalPlot3DB -4 p q - q2

2 p Sin@bD -4 p q - q2

2 p Sin@bD , 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <F





SphericalPlot3DB -4 p q - q2

2 p Sin@bD -4 p q - q2

2 p Sin@bD , 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<FComputationalGeometry`Methods`SpatialSearch::spoutbounds :

--


H8-

134.929,-

33.9566<L





General::stop :

Further output of ComputationalGeometry`Methods`SpatialSearch::spoutbounds will be suppressed

during this calculation. à





SolveB - Â ==

r 1 -HvL2

c2

q

1-HvL

2

c2

4 p r - r q


4 p q - q2

-2 p Sin@bD

4 p q - q2

, bF

Solve::ifun :

Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete

solution information. à

::b Ø ArcSinB 4 p - q q

2 pF>>

"Velocity" Variable Configurations

SolveB - Â == -

r 1 -HvL2

c2

q

1-HvL2

c2

4 p r - r q

2 p r Sin@bD , vF

::v Ø -1. - 3.54814 µ 10

18- 1.12941 µ 10

18q Csc@bD2 + 8.98755 µ 10

16q2 Csc@bD2

- 39.4784 - 12.5664 q Csc@bD2 + q2 Csc@bD2>,

:v Ø- 3.54814 µ 10

18- 1.12941 µ 10

18q Csc@bD2 + 8.98755 µ 10

16q2 Csc@bD2

- 39.4784 - 12.5664 q Csc@bD2 + q2 Csc@bD2>>





SphericalPlot3DBI1.`,I- 3.5481432270250993`*^18-

1.1294090667581471`*^18q Csc@bD2 + 8.987551787368176`*^16 q2 Csc@bD2MM ì

- 39.47841760435743` - 12.566370614359172` q Csc@bD2 + q2 Csc@bD2 ,

8q

,-

2p

, 2p

<, 8b

,- p

ê 2,p

ê 2<F





SphericalPlot3DBI,I- 3.5481432270250993`*^18-

1.1294090667581471`*^18q Csc@bD2 + 8.987551787368176`*^16 q2 Csc@bD2MM ì

- 39.47841760435743` - 12.566370614359172` q Csc@bD2 + q2 Csc@bD2 ,

8q

,-

2p

, 2p

<, 8b

,- p

ê 2,p

ê 2<F

SolveB - Â ==

r 1 -HvL2

c2

q

1-HvL2

c2

4 p r - r q


4 p q - q2

-2 p Sin@bD

4 p q - q2

, vF

SolveB - Â ==

r 1 -HvL2

c2

q

1-HvL2

c2

4 p r - r q


4 p q - q2

-2 p Sin@bD

4 p q - q2

, vF





::v Ø - 1. 1.15444 µ 1082

+1.02759 µ 10

6612.5664 q - 1. q2 Csc@bD

12.5664 - 1. q-

8.17729 µ 1064

q 12.5664 q - 1. q2 [email protected] - 1. q - 3.67469 µ 10

81

q Csc@bD2

+

2.92423 µ 1080

q2 Csc@bD2 -

1

12.5664 - 1. qI0. + 2.57578 µ 10

66ÂM 12.5664 q - 1. q

2

Csc@bD -1. 12.5664 q - 1. q2 Sin@bD

H12.5664 - 1. qL q+

1

12.5664 - 1. qI0. + 2.04974 µ 10

65ÂM

q 12.5664 q - 1. q2 Csc@bD -

1. 12.5664 q - 1. q2 [email protected] - 1. qL q

-

I0. + 4.09949 µ 1065

ÂM q Csc@bD2 -1. 12.5664 q - 1. q2 Sin@bD

H12.5664 - 1. qL q+

I0. + 3.26227 µ 1064

ÂM q2 Csc@bD2 -


ì

1.28449 µ 1065

- 4.08865 µ 1064

q Csc@bD2 + 3.25364 µ 1063

q2

Csc@bD2 >,

:v Ø 1.15444 µ 1082

+1.02759 µ 10

6612.5664 q - 1. q2 Csc@bD

12.5664 - 1. q

-

8.17729 µ 1064

q 12.5664 q - 1. q2 [email protected] - 1. q

- 3.67469 µ 1081

q Csc@bD2 +

2.92423 µ 1080

q2

Csc@bD2 -1

12.5664 - 1. qI0. + 2.57578 µ 10

66ÂM 12.5664 q - 1. q

2

Csc@bD -1. 12.5664 q - 1. q2 Sin@bD

H12.5664 - 1. qL q+

1

12.5664 - 1. qI0. + 2.04974 µ 10

65ÂM





q 12.5664 q - 1. q2 Csc@bD -


-

I0. + 4.09949 µ 10

65

ÂM q Csc@bD2

-

1. 12.5664 q - 1. q2 [email protected] - 1. qL q +

I0. + 3.26227 µ 1064

ÂM q2

Csc@bD2 -1. 12.5664 q - 1. q2 Sin@bD

H12.5664 - 1. qL q ì

1.28449 µ 1065

- 4.08865 µ 1064

q Csc@bD2 + 3.25364 µ 1063

q2 Csc@bD2 >>

SphericalPlot3DB- 1.` 1.1544381966263221̀ *^82 +

1.0275885793493724`*^66 12.566370614359172` q - 1.` q2 [email protected]`- 1.` q

-

8.177290093411547`*^64 q 12.566370614359172` q - 1.` q2 [email protected]`- 1.` q

-

3.6746909097434513`*^81q Csc@bD2 + 2.9242261131026207`*^80q2 Csc@bD2 -

1

12.566370614359172`- 1.` qH0.` + 2.5757825876850383`*^66ÂL

12.566370614359172` q - 1.` q2 Csc@bD

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` qL q+

1

12.566370614359172`- 1.` q

H0.` + 2.0497426558005358`*^65ÂL q 12.566370614359172` q - 1.` q2

Csc@bD -1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172` - 1.` qL q-

H0.` + 4.0994853116010716`*^65ÂL q Csc@bD2

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` qL q

+

H0.` + 3.262266757369647`*^64 Â

L

q2 Csc@bD2 -

1.` 12.566370614359172` q - 1.` q2 [email protected]`- 1.` qL q

ì

I,I1.2844857241867155`*^65- 4.0886450467057735`*^64q Csc@bD2 +

3.2536403486570855`*^63q2 Csc@bD2MM, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F





SphericalPlot3DB- 1.` 1.1544381966263221̀ *^82 +

1.0275885793493724`*^66 12.566370614359172` q - 1.` q2 Csc

@b

D12.566370614359172`- 1.` q-


-

3.6746909097434513`*^81q Csc@bD2 + 2.9242261131026207`*^80q2 Csc@bD2 -

1

12.566370614359172`- 1.` qH0.` + 2.5757825876850383`*^66ÂL

12.566370614359172` q - 1.` q2 Csc@bD

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` qL q

+1

12.566370614359172`- 1.` q

H0.` + 2.0497426558005358`*^65ÂL q 12.566370614359172` q - 1.` q2

Csc@bD -1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172` - 1.` qL q-

H0.` + 4.0994853116010716`*^65ÂL q Csc@bD2

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` qL q+ H0.` + 3.262266757369647`*^64 ÂL

q2 Csc@bD2 -

1.` 12.566370614359172` q - 1.` q2 [email protected]`- 1.` qL q ì

I,I1.2844857241867155`*^65- 4.0886450467057735`*^64q Csc@bD2 +

3.2536403486570855`*^63q2 Csc@bD2MM, 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <F





SphericalPlot3DB

1.1544381966263221`*^82+1.0275885793493724`*^66 12.566370614359172` q - 1.` q2 Csc@bD

12.566370614359172`- 1.` q-


-

3.6746909097434513`*^81q Csc@bD2 + 2.9242261131026207`*^80q2 Csc@bD2 -

1

12.566370614359172`- 1.` qH0.` + 2.5757825876850383`*^66ÂL

12.566370614359172` q - 1.` q2 Csc@bD -

1.` 12.566370614359172` q - 1.` q2 [email protected]` - 1.` qL q

+

1

12.566370614359172`- 1.` q

H0.` + 2.0497426558005358`*^65Â

Lq

12.566370614359172` q - 1.` q2 Csc@bD -


-

H0.` + 4.0994853116010716`*^65ÂL q Csc@bD2

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` qL q+ H0.` + 3.262266757369647`*^64 ÂL

q2 Csc

@b

D2

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` q

Lq

ì I,I1.2844857241867155`*^65- 4.0886450467057735`*^64q Csc@bD2 +

3.2536403486570855`*^63q2 Csc@bD2MM,

8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <, PlotStyle Ø [email protected]





SphericalPlot3DB

1.1544381966263221`*^82+1.0275885793493724`*^66 12.566370614359172` q - 1.` q2 Csc@bD

12.566370614359172`- 1.` q-


-

3.6746909097434513`*^81q Csc@bD2 + 2.9242261131026207`*^80q2 Csc@bD2 -

1

12.566370614359172`- 1.` qH0.` + 2.5757825876850383`*^66ÂL

12.566370614359172` q - 1.` q2 Csc@bD -


+

1

12.566370614359172`- 1.` q

H0.` + 2.0497426558005358`*^65Â

Lq

12.566370614359172` q - 1.` q2 Csc@bD -


-

H0.` + 4.0994853116010716`*^65ÂL q Csc@bD2

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` qL q+ H0.` + 3.262266757369647`*^64 ÂL

q2 Csc

@b

D2

-1.` 12.566370614359172` q - 1.` q2 Sin@bD

H12.566370614359172`- 1.` q

Lq

ì I,I1.2844857241867155`*^65- 4.0886450467057735`*^64q Csc@bD2 +

3.2536403486570855`*^63q2 Csc@bD2MM,

8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<, PlotStyle Ø [email protected]





c := 2.99792458 * H10^8L

SolveB - Â ==2 p r Sin@bD

r 1 -HvL2

c2

q

1-HvL2

c2

4 p r - r q

-2 p Sin@bD

4 p q - q2

-2 p Sin@bD

4 p q - q2

, vF

SolveB - Â == - -2 p r Sin@bD

r 1 -HvL2

c2

q

1-HvL2

c2

4 p r - r q

, vF

::v Ø -1. - 6.91664 µ 10

33q + 5.50409 µ 10

32q2 + 2.17293 µ 10

34Sin@bD2

- 7.6958 µ 1016

q + 6.12412 µ 1015

q2 + 2.41771 µ 1017

Sin@bD2>,

:v Ø- 6.91664 µ 10

33

q + 5.50409 µ 1032

q2 + 2.17293 µ 1034

Sin@bD2

- 7.6958 µ 1016

q + 6.12412 µ 1015

q2 + 2.41771 µ 1017

Sin@bD2>>





SphericalPlot3DAI,I- 6.916640561054567`*^33 q + 5.504087674408674`*^32 q

2+ 2.1729267174130213`*^34 Sin@bD2MM ë

I,I- 7.695800507960096`*^16 q + 6.124123459454841`*^15 q2

+ 2.4177070339300032`*^17 Sin@bD2MM,

8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<E





SphericalPlot3DB. - 6.916640561054567`*^33 q + 5.504087674408674`*^32 2 p + p

2- p

2 Sin@bD2 2

+

2.1729267174130213`*^34 Sin

@b

D2

ì I,I- 7.695800507960096`*^16 q + 6.124123459454841`*^15 q2

+ 2.4177070339300032`*^17 Sin@bD2MM,

8b, - p ê 2, p ê 2<, 8q, - 2 p , 2 p <F





SphericalPlot3DB. - 6.916640561054567`*^33 q + 5.504087674408674`*^32 2 p + p

2- p

2 Sin@bD2 2

+

2.1729267174130213`*^34 Sin

@b

D2

ì I,I- 7.695800507960096`*^16 q + 6.124123459454841`*^15 q2

+ 2.4177070339300032`*^17 Sin@bD2MM,

8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F





SphericalPlot3DB . - 6.916640561054567`*^33 2 p + p 2

- p 2 Sin@bD2 +

5.504087674408674`*^32 2 p + p 2

- p 2 Sin@bD2 2

+ 2.1729267174130213`*^34 Sin@bD2 ì

I,I- 7.695800507960096`*^16 q + 6.124123459454841`*^15

Hq

L2

+

2.4177070339300032`*^17 Sin@bD2MM, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F





SphericalPlot3DB- - 1.1294090667581471`*^18 2 p + p

2- p

2 Sin@bD2 + 8.987551787368176`*^16 q2

+

3.5481432270250993`*^18 Sin@bD2 ì - 12.566370614359172` q + q

2

+ 39.47841760435743` Sin@bD2

, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F





SphericalPlot3DB. - 1.1294090667581471`*^18q + 8.987551787368176`*^16 2 p + p

2- p

2 Sin@bD2 2

+

3.5481432270250993`*^18 Sin

@b

D2

ì - 12.566370614359172` q + q

2+ 39.47841760435743` Sin@bD2 , 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F





SphericalPlot3DB- - 1.1294090667581471`*^18 2 p + p

2- p

2 Sin@bD2 + 8.987551787368176`*^16 HqL2 +

3.5481432270250993`*^18 Sin@bD2 ì

. - 12.566370614359172` 2 p + p 2

- p 2 Sin@bD2 + 2 p + p

2- p

2 Sin@bD22

+

39.47841760435743` Sin@bD2 , 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F

Power::infy : Infinite expression1

0.encountered. à


0.encountered. à


0.

encountered. à

General::stop : Further output of Power::infy will be suppressed during this calculation. à


velocity configurations and phenomenological description of the square root of negative i © parker...

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