Revision of Mathematical Extension of Newman's Theory

[kmarinas86]

linear mass density=distributed mass/distance of distribution

applied voltage=capacitive voltage drop+resistive voltage drop+inductive voltage drop

capacitive voltage drop=(1/capacitance)*charge
resistive voltage drop=resistance*current
inductive voltage drop=inductance*(change of current/change of time)

capacitive voltage drop=(1/capacitance)*linear charge density*distance
resistive voltage drop=resistance*linear charge density*velocity
inductive voltage drop=inductance*linear charge density*acceleration

linear mass density*velocity=mass flow rate
linear mass density*velocity^2=force
linear mass density*velocity^3=power

resistive voltage drop=resistance*(charge/mass)*mass flow rate
real power=resistance*(charge/mass)^2*mass flow rate^2

distance/velocity=energy/power
velocity/acceleration=power/(change of power/change of time)

distance/velocity=angular momentum/torque
velocity/acceleration=torque/(change in torque/change in time)

If capacitive voltage drop=applied voltage

resistive voltage drop=-inductive voltage drop
velocity/acceleration=-inductance/resistance

apparent power=voltage*current
torque=magnetic flux*current
real power=resistance*current^2

voltage/magnetic flux=apparent power/torque
resistance*current/magnetic flux=real power/torque
resistance/inductance=real power/torque

A GREATER INDUCTANCE FOR A GIVEN RESISTANCE INCREASES TORQUE OUTPUT (ANGULAR MOMENTUM PER UNIT TIME) VS POWER DISSIPATED AS HEAT (JOULES PER UNIT TIME).

inductance/resistance=torque/real power
inductance/resistance=-velocity/acceleration
inductance/resistance=-power/(change in power/change in time)

THE L/R TIME CONSTANT DETERMINES THE RATIO OF MECHANICAL POWER OUTPUT TO RATE CHANGE IN POWER.

torque/real power=-velocity/acceleration
torque/[-velocity/acceleration]=real power
torque*[-acceleration/velocity]=real power
torque*[-force/momentum]=real power
power^2/[angular velocity*-velocity*momentum]=real power
power^2=real power*-velocity*angular velocity*momentum
power^2=real power*mass*[-velocity^3/radius]
[linear mass density*velocity^3]^2=real power*mass*[-velocity^3/radius]
linear mass density=mass/distance
[mass*velocity^3/distance]^2=real power*mass*[-velocity^3/radius]
power=real power*-distance/radius
power=real power*-angle
angle=-power/real power

THE RATIO OF MECHANICAL POWER OUTPUT TO HEAT DISSIPATION IS PROPORTIONAL TO CHANGE IN ANGLE.

power=real power*-energy/torque
-power/energy=real power/torque
-velocity/distance=real power/torque
-torque*velocity/distance=real power
-force*radius*velocity/distance=real power
-force*velocity*radius/distance=real power
-power/angle=real power

torque/real power=-velocity/acceleration
torque/real power=-distance/velocity

velocity/acceleration=distance/velocity
velocity^2=distance*acceleration
power^2=energy*(change in power/change in time)

TO DO A CERTAIN AMOUNT OF WORK, THE RATE CHANGE IN POWER NEEDED INCREASES WITH THE SQUARE OF NEEDED POWER.

real power*[torque/real power]=[-power/angle]*[-velocity/acceleration]
torque=[power/angle]*[velocity/acceleration]
energy=power*[velocity/acceleration]
energy=force*[velocity^2/acceleration]
energy=force*distance

electrical energy=voltage*charge
torque=magnetic flux*current

electrical energy/torque=
[voltage*charge]/[magnetic flux*current]=
[voltage/magnetic flux]*[charge/current]=
[voltage/magnetic flux]*[distance/velocity]=
[voltage/magnetic flux]*[-torque/real power]=
voltage*[-current/real power]=
-apparent power/real power=
-1/power factor

power=real power*-angle
-power/angle=real power
-(power/angular velocity)/(angle/angular velocity)=real power
-(torque)/(angular momentum/torque)=real power
-torque^2/angular momentum=real power
-torque*angular acceleration/angular velocity=real power
-moment of inertia*angular acceleration^2/angular velocity=real power
-[mass*radius^2]*angular acceleration^2/angular velocity=real power
-mass*acceleration^2/angular velocity=real power

COMPARE THE PREVIOUS LINE WITH THE LARMOR FORMULA.

power=[-torque*acceleration/velocity]*-angle
power=energy*acceleration/velocity=linear mass density*velocity^3
force=energy*acceleration/velocity^2=linear mass density*velocity^2
mass flow rate=energy*acceleration/velocity^3=linear mass density*velocity
energy*acceleration=linear mass density*velocity^4
energy*acceleration=mass flow rate*velocity^3
energy*acceleration=force*velocity^2
energy*acceleration=power*velocity

[kmarinas86]

See:

http://academia.wikia.com/wiki/Mechanical_Electric_Theory