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superpig10000
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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.
Here is one example. If you can justify the throw-away in section 1.3, perhaps you can do something similar.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.
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.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?
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.
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.
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.
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.
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.