Why differentiate the constraint equation Xa² + Xb² = L²

[Clever_name]

Homework Statement

See attached picture.

Homework Equations

The Attempt at a Solution

I have the solution, but I'm puzzled by the first step in their solution, which reads

Xa^(2) + Xb^(2) = L^(2)

The solution provider then takes the time derivative of this expression which then produces

2Xa(Xa(dot))+2Xb(Xb(dot)) = 0

where Xa(dot) and Xb(dot) is the Xa or Xb symbol with a dot over it.

Thanks for you're assistance!

 

[Clever_name]

Here is the solution if my explanation was confusing in any way.

 

[Clever_name]

Any help would be greatly appreciated.

 

[haruspex]

I don't understand what's puzzling you. The first line is just Pythagoras' theorem applied to the triangle of which AB is the hypotenuse.

 

[Clever_name]

The line below it, when taking the time derivative of the first line how do they end up with that expression?

 

[haruspex]

If x = x(t), can you write down the expression for (d/dt)x²?

 

[Clever_name]

2x? or x(t)dx/dt = x(t)*x'(t)

 

[Clever_name]

How did you know that x was a function of time?

 

[haruspex]

2x? or x(t)dx/dt = x(t)*x'(t)

No, but each answer you offer is half right. Do you know the chain rule?

 

[Clever_name]

yep, i understand now haruspex, thanks!