How Does Goldstein Derive the Kinetic Energy Equation in Classical Mechanics?

In summary, the conversation discusses the chain rule and its application to the time derivative of (dr/dt)^2. The correct answer to the derivative is given on the right hand side, while the left hand side is already the solution. The conversation ends with the acknowledgement that the rest of Goldstein may be challenging.
  • #1
bengeof
how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 )

Thank You
 
Physics news on Phys.org
  • #2
bengeof said:
how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 )

Thank You

Chain rule.
 
  • Like
Likes Ibix
  • #3
Can you work it out for me explicitly ?
 
  • #4
Can you state the chain rule? Can you apply it to the time derivative of ##(dr/dt)^2##?
 
  • #6
Ibix said:
Can you state the chain rule? Can you apply it to the time derivative of ##(dr/dt)^2##?

2dr/dt . . is that right ?
 
  • #8
bengeof said:
I was able to work out the right hand side. But the left hand side is my problem. .

That makes no sense. The LHS is the answer to the derivative on the RHS. There's nothing to work out on the left.

bengeof said:
2dr/dt . . is that right ?

The stackexchange link I gave you is all about why that is not the answer!
 
  • #9
okay Got it. Thank you so much !
 
  • #10
The rest of Goldstein may present difficulties.
 

Related to How Does Goldstein Derive the Kinetic Energy Equation in Classical Mechanics?

1. What is Classical Mechanics Goldstein Eq3.14?

Classical Mechanics Goldstein Eq3.14 is an equation in the field of classical mechanics that is commonly used to calculate the motion of a system of particles. It is also known as the Lagrange's equation of motion and is derived from the principle of least action.

2. How is Classical Mechanics Goldstein Eq3.14 derived?

Classical Mechanics Goldstein Eq3.14 is derived from the principle of least action, which states that the actual path taken by a system is the one that minimizes the action of the system. This equation is obtained by applying the variational principle to the Lagrangian of the system.

3. What does Classical Mechanics Goldstein Eq3.14 represent?

Classical Mechanics Goldstein Eq3.14 represents the equations of motion of a system of particles. It describes the relationship between the positions, velocities, and accelerations of the particles in the system.

4. Why is Classical Mechanics Goldstein Eq3.14 important?

Classical Mechanics Goldstein Eq3.14 is important because it provides a powerful tool for predicting and analyzing the motion of complex systems. It is widely used in various fields such as physics, engineering, and astronomy to understand the behavior of physical systems.

5. How can I use Classical Mechanics Goldstein Eq3.14?

To use Classical Mechanics Goldstein Eq3.14, you need to have a good understanding of basic physics principles and mathematical concepts such as calculus and vector algebra. You can then apply this equation to solve problems involving the motion of particles in a system, such as projectile motion or planetary motion.

Similar threads

Replies
2
Views
1K
Replies
14
Views
2K
Replies
7
Views
1K
Replies
14
Views
6K
Replies
8
Views
850
  • Mechanics
Replies
11
Views
1K
Replies
1
Views
530
Replies
4
Views
12K
Replies
19
Views
1K
Back
Top