Euler Lagrange Equations for 1 particle in 3-dimensions

In summary, the Euler-Lagrange equations are set to zero for each of the 3 orthogonal coordinates and they are also summed to be equal to zero. The coordinates do not have to be orthogonal in order to write separate E-L equations, as they can be general coordinates not necessarily connected to spatial directions. The main question is whether the Taylor book on Classical Mechanics would explain this well.
  • #1
morangta
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Homework Statement


Do the Euler-Lagrange equations set to zero for each of the 3 orthogonal coordinates or do you sum them all equal to zero. Do the coordinates have to be orthogonal in order to write separate E-L equations? Or is there no such thing as non-orthogonal coordinates to analyze a problem? My main question is the first one.


Homework Equations


d/dt(partial L/partial qi dot) - (partial L/partial qi) = 0?


The Attempt at a Solution


Not sure. Self-study/No textbook here. Thank you for reading my question.
Would the Taylor book on Classical Mechanics explain this well?
 
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  • #2
morangta said:

Homework Statement


Do the Euler-Lagrange equations set to zero for each of the 3 orthogonal coordinates or do you sum them all equal to zero.

You have separate equations for all coordinates. They are general coordinates, needn't be connected to spatial directions.


ehild
 

Related to Euler Lagrange Equations for 1 particle in 3-dimensions

What are Euler Lagrange Equations for 1 particle in 3-dimensions?

The Euler Lagrange Equations for 1 particle in 3-dimensions are a set of mathematical equations used to describe the motion of a single particle in three-dimensional space. They are derived from the principle of least action, which states that the actual path of a particle is the one that minimizes the action integral.

What is the significance of Euler Lagrange Equations in physics?

Euler Lagrange Equations are significant in physics because they provide a mathematical framework for understanding the motion of particles in three-dimensional space. They are used in classical mechanics to describe the dynamics of a system and can be applied to a wide range of physical phenomena, from the motion of planets to the behavior of subatomic particles.

How do the Euler Lagrange Equations relate to Newton's laws of motion?

The Euler Lagrange Equations and Newton's laws of motion are both ways of describing the motion of particles in space. However, while Newton's laws focus on the forces acting on an object, the Euler Lagrange Equations focus on the path the particle takes in order to minimize the action integral.

What are the assumptions made in using Euler Lagrange Equations?

There are several assumptions made when using Euler Lagrange Equations, including assuming that the system is isolated, that there are no external forces acting on the particle, and that the particle's motion is continuous and differentiable.

What are some applications of Euler Lagrange Equations?

Euler Lagrange Equations have many applications in physics, engineering, and mathematics. They are used in classical mechanics to study the motion of particles, in quantum mechanics to describe wave functions, and in control theory to optimize systems. They are also used in fields such as robotics, economics, and computer graphics.

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