Lagrange equation, of a hoop?

Thread starter Shahbakht
Start date Oct 9, 2019
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Lagrange Lagrange equation

In summary, the Lagrange equation of a hoop is a mathematical formula derived using the principle of virtual work, which describes the motion of a circular object rotating around a fixed point. The equation takes into account variables such as mass, radius, moment of inertia, and forces acting on the hoop. It is significant in studying the dynamics of rotating objects and can also be applied to other systems with a finite number of degrees of freedom.

Oct 9, 2019

Shahbakht

Poster warned about not providing an attempt at a solution

Homework Statement: Two equal masses are glued to a massless hoop of radius R that is free to rotate about its center in a vertical plane. The angle between the masses is 2*theta. Find the frequency of small oscillations.

I dont get that if two masses, so where do we take the postion vector from? From the centre?

Relevant Equations: d/dt(dL/dtetha)=dL/dtetga

I couldn't even get the position vector. Help!

Last edited by a moderator: Oct 9, 2019

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Oct 9, 2019

BvU

Science Advisor

Homework Helper

Hello Shahbakht, :welcome:

!

Can you do it for ##\theta = 0## ? We need some effort from you before we are allowed to assist -- see guidelines

1. What is the Lagrange equation of a hoop?

The Lagrange equation of a hoop is a mathematical expression that describes the motion of a hoop, or circular ring, as it rotates around a fixed axis. It takes into account the hoop's mass, moment of inertia, and any external forces acting on it.

2. How is the Lagrange equation derived for a hoop?

The Lagrange equation for a hoop can be derived using the principles of Lagrangian mechanics, which is a mathematical formalism for describing the dynamics of a system. It involves setting up the system's Lagrangian function, which is the difference between its kinetic and potential energy, and then applying the Euler-Lagrange equation to find the equations of motion.

3. What are the variables in the Lagrange equation of a hoop?

The variables in the Lagrange equation of a hoop include the hoop's mass, moment of inertia, and angular position, velocity, and acceleration. It also takes into account any external forces acting on the hoop, such as friction or applied torques.

4. Can the Lagrange equation of a hoop be used for any shape of hoop?

No, the Lagrange equation for a hoop is specifically derived for a circular ring. However, similar equations can be derived for other shapes using the principles of Lagrangian mechanics.

5. How is the Lagrange equation of a hoop used in real-world applications?

The Lagrange equation of a hoop can be used to model and predict the behavior of rotating hoops in various engineering and physics applications. It can also be used to design and optimize mechanisms such as gyroscopes and flywheels. Additionally, the principles of Lagrangian mechanics and the Lagrange equation have broader applications in fields such as robotics, control systems, and quantum mechanics.