Hamilton's equations for double pendulum

In summary, Hamilton's equations for a double pendulum are a set of differential equations derived from Hamilton's principle that describe the motion of a double pendulum system. They provide a complete description of the system's motion, insights into energy conservation and stability, and are derived by applying Hamilton's principle to the Lagrangian of the system. They can only be solved analytically in special cases and have limitations such as idealized conditions and not accounting for external or non-conservative forces.
  • #1
Daniel1992
22
0
At the bottom of the following website are the 4 equations that I am using for a double pendulum simulation.

http://scienceworld.wolfram.com/physics/DoublePendulum.html

The equation for C2 has the variables P1 and P2 and I can't work out what they are.:confused:

Is it a typo and they are meant to be Pθ1 and Pθ2?

Any help would be much appreciated.
 
Physics news on Phys.org
  • #2
Daniel1992 said:
Is it a typo and they are meant to be Pθ1 and Pθ2?
Yes.
 

1. What are Hamilton's equations for a double pendulum?

Hamilton's equations for a double pendulum are a set of differential equations that describe the motion of a double pendulum system. They are derived from Hamilton's principle, which states that the motion of a system can be described by minimizing an action integral.

2. What is the significance of Hamilton's equations for a double pendulum?

Hamilton's equations for a double pendulum provide a complete description of the system's motion and allow for predicting its future behavior. They also provide insight into the system's energy conservation and stability.

3. How are Hamilton's equations for a double pendulum derived?

Hamilton's equations for a double pendulum are derived by applying Hamilton's principle to the Lagrangian of the system, which is the difference between the system's kinetic and potential energies. This results in a set of two second-order differential equations.

4. Can Hamilton's equations for a double pendulum be solved analytically?

In most cases, Hamilton's equations for a double pendulum cannot be solved analytically and require numerical methods for solutions. However, in some special cases, such as when the pendulum lengths are equal, analytic solutions are possible.

5. What are the limitations of Hamilton's equations for a double pendulum?

Hamilton's equations for a double pendulum assume idealized conditions, such as a frictionless and massless system. They also do not take into account external forces or non-conservative forces. Additionally, they may become complex and difficult to solve for more complex systems.

Similar threads

Double Pendulum Potential Energy
    • Mechanics
Replies
4
Views
1K
Equations of motion of a double pendulum
    • Mechanics
Replies
2
Views
3K
Derivation of time period for physical pendula without calculus
    • Introductory Physics Homework Help
Replies
3
Views
686
Motion Equations by Newton's Formalism for a Double Pendulum
    • Mechanical Engineering
Replies
3
Views
1K
B Calculating g with a Conical Pendulum
    • Classical Physics
Replies
3
Views
2K
Angular acceleration of Pendulum equation
    • Mechanics
Replies
3
Views
13K
Physics IA: Distance B/w Pendulum & Alum. Block, Finding Damping Coefficient
    • Introductory Physics Homework Help
Replies
9
Views
1K
Determining linear velocity of pendulum
    • Mechanics
Replies
4
Views
4K
Simple Harmonic Motion/Period of a Physical Pendulum
    • Mechanics
Replies
11
Views
3K
How Do You Model a Horizontal Double Pendulum with External Forces?
    • Mechanics
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top