Free body diagram for hinged rods

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SUMMARY

The discussion revolves around the dynamics equations for a double pendulum setup without using Lagrange methods. The user encounters challenges in applying a Free Body Diagram (FBD) at the pivot point where two rods connect, specifically questioning the absence of mass at this junction. The user derives the equation T1 = T2*cos(a - b) but finds discrepancies when comparing it to established equations from a referenced paper that includes a mass. This indicates a misunderstanding in applying FBD principles in the absence of mass at the pivot.

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joes1987
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Hello all!

First post! I've been meaning to join this board for a while. I'm an electronic engineer with interests in physics.

I set myself the challenge of trying to obtain the dynamics equations for a double pendulum setup without using Lagrange. (configuration in attached picture)

The issue I seem to be having centres around the point at which the 2 rods are connected. I don't have a mass at this point. Does this mean I cannot use a normal Free Body Diagram? If I am allowed to, then I have only 2 forces at this pivot point (I think!) - the tensions of each rod. However, I was looking at this link: http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/DoublePendulum.pdf
which does a pretty similar problem using Newtons laws, the only difference is that they have a mass between the two rods. However, when I look at their equations (32) and (33) which are Newton's laws on the free-body diagram of this junction, and reduce the mass (m1) to zero, I don't get the same equation as I have.

When I work it out independently, I get: T1 = T2*cos(a - b), whereas the equations from that paper just don't make any sense when I set m1 = 0.

Am I doing something silly?

Thanks!
 

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joes1987 said:
Am I doing something silly?
Probably, but if you don't show us exactly what you did, we cannot be sure.
 

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