What do you do when time is present in Lagragian Equation?

In summary, the conversation discusses setting up a Lagrangian equation involving time t and the confusion of how to solve it. The person asks for help since they only know how to solve Lagrangian equations without time. A document is referenced and the question is asked if time is important in the differentiation process. The response is that if (dL/dq dot) is a function of time, then it should be taken into consideration. The person is advised to follow the example in the document.
  • #1
superpig10000
8
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I set up a Lagragian equation that involves time t. What do I do? I only know how to solve Lagragian equation in the absence of time. Please help.
 
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  • #2
superpig10000 said:
I set up a Lagragian equation that involves time t. What do I do? I only know how to solve Lagragian equation in the absence of time. Please help.
Here is one example. If you can justify the throw-away in section 1.3, perhaps you can do something similar.

http://physics.technion.ac.il/~avron/classical-mechanics/kapitza-wbct.pdf
 
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  • #3
I understand the throw away, but when I differentiate

dL/dq - d/dt (dL/dq dot) = 0

do I care about time at all?
 
  • #4
superpig10000 said:
I understand the throw away, but when I differentiate

dL/dq - d/dt (dL/dq dot) = 0

do I care about time at all?
If your (dL/dq dot) is a function of time, then why would you not care? I think once you have the simplified Lagarangian you do what you always do. It's been a long time since I did this stuff, but I don't see any reason to deviate from the example.
 

1. What is the Lagrangian Equation and why is time present in it?

The Lagrangian Equation is a mathematical equation used in classical mechanics to describe the motion of a system of particles. It takes into account the kinetic and potential energies of the particles in the system. Time is present in the Lagrangian Equation because it is a fundamental component of the equation and is necessary for accurately describing the motion of the system over time.

2. How is time represented in the Lagrangian Equation?

Time is represented in the Lagrangian Equation through the use of the variable t, which represents the independent variable of time. It is used in the equation to determine the rate of change of the system's position and velocities over time.

3. Can the Lagrangian Equation be used for systems with changing velocities over time?

Yes, the Lagrangian Equation can be used for systems with changing velocities over time. This is because the equation takes into account the rate of change of the system's position and velocities, which can vary over time.

4. How does the Lagrangian Equation account for the effects of time on a system?

The Lagrangian Equation takes into account the effects of time on a system by incorporating the concept of "virtual displacements." These are infinitesimal changes in the system's position and velocities over time, which are used to calculate the system's kinetic and potential energies at any given moment.

5. Are there any limitations to using the Lagrangian Equation when time is present?

While the Lagrangian Equation is a powerful tool for describing the motion of systems with changing velocities over time, it does have its limitations. It is most effective for systems in which the kinetic and potential energies are dependent only on the positions and velocities of the particles, and not on their accelerations. Additionally, it is not suitable for systems where dissipation of energy occurs, such as in systems with friction or other external forces.

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