2 methods same answer dynamics

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SUMMARY

The discussion focuses on two methods for analyzing dynamics involving two masses and torques, specifically referencing the MIT OpenCourseWare approach. The first method involves summing forces and torques to derive angular momentum changes, while the second method utilizes differential equations for each mass, incorporating parameters like damping and gravitational forces. The user expresses confusion about the advantages of the torque/angular momentum approach compared to their traditional method. The conversation suggests that the torque method may be more suitable for problems involving Lagrange equations and generalized forces.

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  • Understanding of Newtonian mechanics and forces
  • Familiarity with angular momentum concepts
  • Knowledge of differential equations in physics
  • Basic grasp of Lagrangian mechanics
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  • Study the MIT OpenCourseWare dynamics course for a comprehensive understanding of the torque method
  • Learn about Lagrange equations and their application in dynamics
  • Explore the concept of generalized forces and their role in mechanical systems
  • Review examples of systems analyzed using both torque and force methods for comparative insights
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Physics students, mechanical engineers, and anyone interested in advanced dynamics and the application of Lagrangian mechanics in solving complex problems.

fahraynk
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In this dynamics MIT open coarseware they are teaching this method where I sum forces on first mass, sum forces on second mass and then sum of torques = change in angular momentum.

upload_2017-3-24_4-32-20.png


The way I originally learned it was just to look at it and do this :
MX1''=-KX1 - BX1' + M2G/L*(X2-X1) <--(sin(theta)=X2-X1/L for small angles)
MX2''=-M2G/L * (X2-X1)
Why would I want to use the torque/angular momentum equations? Whats the benefit/difference? I am lost and do not see the bridge between what I have been doing and what he is doing.

If interested, simply put this into Youtube search : R7: Cart and Pendulum, Direct Method (don't want to add a link on forum because not sure if there is anti spam or something)
 
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I would say that this problem is rather for the Lagrange equations with generalized force in the right hand side. The generalized force is due to the damper b
 

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