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Optimize release angle of a trebuchet (highschool project)?

Posted 24 days ago
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Hi, i'm new to using Mathematica and i'm trying to optimize the release angle of a trebuchet using Lagrangian multipliers. I have read much about it and I have come to understand how it is calculated. I ended up going with mathematica to solve the calculations since it is quite a task by hand. I've got a trebuchet with a counterweight pendulum, and a projectile on the end of a sling: enter image description here

i am basing my calculations on the following info and equations

I have attached my attempt in solving this using Mathematica. I have tested the method using a much simpler example with success(also attached). What I think is going wrong for me is the notation of the angular velocity and how i represent time.

I would like to find the angle(phi) and time where velocity(kinetic energy) of the projectile is the greatest with a potential energy constraint of 100.

My approach was to use L(the,phi,t)=f(the,phi)−λ2(g1(the,phi)−c1)-λ2(g2(the,phi)−c2)


finding the gradient of 0=f(the,phi)−λ1(g1(the,phi)−c1)-λ2(g2(the,phi)−c2)

f(the,phi)=kinetic energy being optimized, g1(the,phi)=potential energy, c1=100, g2(the,phi)=contreint for sling, c1=0

Thanks in advance

3 Replies
Posted 24 days ago

Maybe two of my Wolfram Demonstrations can help?

"Trebuchet Baliistics"

"Optimizing the Counterweight Trebuchet"

thanks for the reply and links. would you by any chance have en example of the calculations for solving using ND solve that i can have a look at? or a more in depth discription? in the second link do you put the kineic and potential energy equations into L(x,y,…,λ)=f(x,y,…)−λ(g(x,y,…)−c) and simplify? then find the gradiant? would the next step just be placing the constants into the three equations and solving the simultaneous equation for a t value?

Posted 24 days ago

All I have on this is in the details of these demonstration.

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