Geodesic equation proof confusing me

In summary, a geodesic equation is a mathematical formula that describes the shortest path between two points on a curved surface. It is important for understanding the behavior of objects in space, and is derived from the principles of calculus and differential geometry. However, the proof of the geodesic equation can be confusing due to its use of advanced mathematical concepts and complex equations. One common misconception is that it only applies to objects moving in a vacuum, but it can also be used in other situations. To better understand the proof, a strong foundation in mathematics and additional resources may be helpful.
  • #1
Superposed_Cat
388
5
Hi all, I was looking through this proof and have no idea where the "u" comes from., any help apreciated.
splaystyle+++%5Cfrac%7Bd%5E%7B2%7Dx%5E%7Bm%7D%7D%7Bd%5Ctau%5E%7B2%7D%7D+&bg=eedbbd&fg=000000&s=0.png
latex.png
latex.png

http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++&bg=eedbbd&fg=000000&s=0
latex.png
latex.png

http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++&bg=eedbbd&fg=000000&s=0
latex.png
latex.png

http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++&bg=eedbbd&fg=000000&s=0
latex.png
latex.png

http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++&bg=eedbbd&fg=000000&s=0
latex.png
latex.png

http://s0.wp.com/latex.php?latex=%5Cdisplaystyle++&bg=eedbbd&fg=000000&s=0
latex.png
latex.png

where
latex.png
 
Last edited:
Physics news on Phys.org
  • #2
It looks like they have defined ##u^m\equiv \frac{dx^m}{d\tau}##
 
  • Like
Likes Superposed_Cat

1. What is a geodesic equation and why is it important?

A geodesic equation is a mathematical formula that describes the shortest path between two points on a curved surface. It is important because it helps us understand the behavior of objects in space, such as planets orbiting around a sun or satellites orbiting around Earth.

2. How is the geodesic equation derived?

The geodesic equation is derived from the principles of calculus and differential geometry. It involves finding the path that minimizes the length between two points on a curved surface, taking into account the curvature of the surface itself.

3. Why is the proof of the geodesic equation confusing?

The proof of the geodesic equation can be confusing because it requires a strong understanding of advanced mathematical concepts, such as tensor calculus and differential geometry. It also involves complex equations and notation that may be difficult to follow for those without a strong background in mathematics.

4. What are some common misconceptions about the geodesic equation proof?

One common misconception is that the geodesic equation only applies to objects moving in a vacuum. In reality, it can also be used to describe the motion of objects in any curved space, such as on a planet's surface or in the presence of other forces.

5. How can I better understand the geodesic equation proof?

To better understand the geodesic equation proof, it is helpful to have a strong foundation in mathematics, particularly in calculus and differential geometry. It may also be helpful to seek out additional resources, such as textbooks or online tutorials, that break down the proof step by step and provide examples for better understanding.

Similar threads

I L due to Azimuthal (1/r)x(1/r^2) Poynting vector components?
    • Classical Physics
Replies
1
Views
1K
A Understading geodesic equation/code for (+1,-1,-1,-1) Sch. Metric
    • Special and General Relativity
Replies
1
Views
531
I Learn About Conservation Law & Geodesic Equation
    • Special and General Relativity
Replies
10
Views
1K
Upward and downward movement of a rocket with the equation of motion
    • Introductory Physics Homework Help
Replies
13
Views
953
MHB Solving Rational ODE's of the form (ax+by+c) dx+(ex+fy+g) dy=0.
    • Differential Equations
Replies
1
Views
5K
I Perturbation to Flat Space Metric: Geodesic Equation
    • Special and General Relativity
Replies
6
Views
1K
General relativity - Using Ricc and Weyl tensor to find the area
    • Advanced Physics Homework Help
Replies
1
Views
978
Weak Field Approx, algebra geodesic equation
    • Special and General Relativity
Replies
28
Views
3K
How Do Sign Conventions Affect Equations in Newton's Second Law?
    • Thermodynamics
Replies
16
Views
2K
A Equations for computing null geodesics in Schwarzschild spacetime
    • Special and General Relativity
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top