hello every one i have this pendulum: i need to stabilize the pendulum in the inverted position , i need to know the potential energy for the pendulum , i read several articles in each one i have a different equation : [itex]V=mgl_{p}cos\alpha[/itex] [itex]V=-mgl_{p}cos\alpha[/itex] [itex]V=mgl_{p}(1-cos\alpha)[/itex] [itex]V=mgl_{p}(cos\alpha-1)[/itex] Now i'am really confused which equation is the correct one? Please help me
What are you taking as your reference level? (Where PE = 0.) The pivot? The gravitational PE is given by mgΔy, where Δy is measured from your chosen reference level. Using that you should be able to pick the correct formula.
[itex]P.E=0[/itex] at the vertical position ([itex]\alpha=0[/itex] from the vertical line in the picture above), now which formula should i use : [itex]P.E=mgl_{p}(1-cos\alpha)[/itex] or [itex]P.E=mgl_{p}(cos\alpha-1)[/itex]
Using the vertical position as your reference, Δy will be negative for any nonzero angle. The second of those is the one you want.
so: [itex]\Delta y=[/itex](center of mass level-reference level) not the other way around , am i correct?
Δy is measured from the PE = 0 reference point. Another way to write the PE is mgy, where y is the vertical position of the center of mass and y = 0 is the PE = 0 point. Since you are choosing the reference level to be where the pendulum is vertical (the angle is zero) and thus the mass is at its highest point, all values for y and thus PE for non-zero angles will be negative since they are below that point.