Lagrangian Mechanics Question: A Yoyo radius a and b

Click For Summary
SUMMARY

The discussion centers on deriving the Lagrangian equation of motion for a yoyo falling straight down while unwinding. The kinetic energy is divided into two components: translational kinetic energy, represented as \( \frac{1}{2} m \dot{Y}^2 \), and rotational kinetic energy, expressed as \( \frac{1}{2} I \dot{\Theta}^2 \). The potential energy is defined as \( U = mgy \). The resulting Lagrangian is formulated as \( L = \frac{1}{2} m \dot{Y}^2 + \frac{1}{2} I \dot{\Theta}^2 - mgy \), with generalized coordinates being \( \Theta \) and \( Y \).

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with kinetic and potential energy concepts
  • Knowledge of rotational dynamics and moment of inertia
  • Ability to apply generalized coordinates in mechanics
NEXT STEPS
  • Study the derivation of Lagrangian equations in classical mechanics
  • Explore the application of generalized coordinates in complex systems
  • Learn about constraints in Lagrangian mechanics
  • Investigate the relationship between translational and rotational motion
USEFUL FOR

This discussion is beneficial for physics students, mechanical engineers, and anyone studying classical mechanics, particularly those interested in Lagrangian dynamics and rotational motion analysis.

BiGubbs
Messages
1
Reaction score
0

Homework Statement


A yoyo falls straight down unwinding as it goes, assume has inner radius a, outer radius b and Inertia I. What is the generalised coordinates and the lagrangian equation of motion?

Homework Equations


L=T-U where T is kinetic energy and U is potential

The Attempt at a Solution


So i assumed that there are 2 parts of kinetic energy, downwards and rotational, the downwards:

1/2 m Y(dot)^2

and rotational

1/2 I (Theta)(dot)^2 .

Potential is simply: mgy

This gives a lagrangian of L= 1/2 m Y(dot)^2 + 1/2 I (Theta)(dot)^2 - mgy
with general co-ords theta and Y, is this correct?
 
Physics news on Phys.org
So far so good.
In which direction is your generalized coordinate y increasing? Are there any constraints to be imposed? Where is your zero of potential energy? Where is your equation of motion?
 

Similar threads

Deriving the Hamiltonian of a system given the Lagrangian
  • · Replies 2 ·
Replies
2
Views
1K
Determine the Lagrangian for the particle moving in this 3-D cos^2 well
  • · Replies 6 ·
Replies
6
Views
2K
Using Lagrangian to show a particle has a circular orbit
  • · Replies 4 ·
Replies
4
Views
3K
Plane pendulum: Lagrangian, Hamiltonian and energy conservation
  • · Replies 6 ·
Replies
6
Views
3K
Lagrangian of a double pendulum, finding kinetic energy
  • · Replies 3 ·
Replies
3
Views
3K
Watt Rotational Speed Regulator's Lagrangian
  • · Replies 6 ·
Replies
6
Views
2K
Point transformation for a constrained particle
  • · Replies 7 ·
Replies
7
Views
2K
Lagrangian mechanics, system of a spring and a pendulum
  • · Replies 21 ·
Replies
21
Views
5K
Constraint force using Lagrangian Multipliers
  • · Replies 6 ·
Replies
6
Views
3K
Question about using the Lagrangian for a spinning rubber band problem
  • · Replies 25 ·
Replies
25
Views
4K