What is the Equation for increasing Periapsis at Apoapsis ?

[5kinflute]

Good morning,

I have a problem which I can't comprehend. I use the Trajectory Formula / Conic Section Equation of an orbit and I graphed it from 0 < Θ < 2π and with it, when I increase my velocity , my apoapsis increases as shown in the image:

 

When I set my true anomaly to 180 degrees (apoapsis), and increase velocity... my periapsis doesn't increase in height but apoapsis continues to increase. 
My desired behavior is:

In KSP, the periapsis angle and apoapsis angles both shifts to the correct values, but how is this done mathematically? 

Thanks,

5kinflute

Edited October 2, 2022 by 5kinflute
wrong pictures

[Shpaget]

Vis viva equation may be what you're looking for.

https://en.m.wikipedia.org/wiki/Vis-viva_equation

[tomf]

To elaborate I would get the sma of the current orbit and use vis Viva to get my velocity at pe, then I would get the sma of the desired orbit and calculate the required velocity at pe

[5kinflute]

thanks guys, I also realized this is possible because of specific mechanical energy which is constant

energy (constant) = kinetic energy + potential

im really new to orbital mechanics so this went over my head

Edited October 3, 2022 by 5kinflute

[Dinlink]

I have done a detailed walkthrough of an example calculation on this thread:

 

Hole you find it useful!

[kerbiloid]

On 10/3/2022 at 8:48 AM, 5kinflute said:

because of specific mechanical energy

The angular momentum is also constant. It's another part of because.