I Uniquely Defined Accelerations

  • I
  • Thread starter Thread starter LukasMont
  • Start date Start date
AI Thread Summary
The discussion centers on the interpretation of a passage from Landau's book regarding the relationship between coordinates, velocities, and accelerations in a physical system. It is argued that knowing positions and velocities alone does not uniquely determine accelerations without additional information, such as forces acting on the system. Participants suggest that Landau's reference to "experience" implies that classical forces depend on the first derivative of position, thus linking acceleration to position and velocity. The conversation highlights the complexity behind Landau's seemingly straightforward conclusions, indicating deeper implications in his work. Ultimately, the discussion emphasizes the need for careful interpretation of Landau's statements in the context of classical mechanics.
LukasMont
Messages
6
Reaction score
3
From Landau's book, here's the following extract:

"If all the co-ordinates and velocities are simultaneously specified, it is known from experience that the state of the system is completely determined and that its subsequent motion can, in principle, be calculated. Mathematically this means that, if all the co-ordinates q and q˙ are given at some instant, the accelerations q¨ at that instant are uniquely defined".

I don't understand how that can be the case. Knowing the positions and velocities in a given moment allow me to calculate the new positions at a dt time afterwards, if accelerations are all zero. If not, I'll need to know the accelerations from some other source, like knowing the forces acting on the system, etc. I don't see how merely having positions and accelerations in a given moment gives you the accelerations in that moment as well.
 
Physics news on Phys.org
I think in this case Landau has a little more in the back of his mind. I would interpret "from experience" to mean something like all the classical forces we know depend on at most the first derivative of position. In that sense, any acceleration at a particular time is determined by the position or velocity at that time.
 
Reply
  • Like
Likes vanhees71 and LukasMont
Haborix said:
I think in this case Landau has a little more in the back of his mind. I would interpret "from experience" to mean something like all the classical forces we know depend on at most the first derivative of position. In that sense, any acceleration at a particular time is determined by the position or velocity at that time.
@Haborix, that was my interpretation as well...but I thought it would be better to bring the topic into discussion, since sometimes in Landau's books he makes this fast, "simple" conclusions which are actually deeper than his tone may convey. Thanks for your input!
 
LukasMont said:
@Haborix, that was my interpretation as well...but I thought it would be better to bring the topic into discussion, since sometimes in Landau's books he makes this fast, "simple" conclusions which are actually deeper than his tone may convey. Thanks for your input!
That's definitely a good instinct to have when you go through Landau, but I think in this instant he's just getting the reader primed to see how these facts fall out naturally from extremizing the action.
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »

Thread 'Free fall of person in a sled to direct horizontal motion by atmospheric resistance'

Let there be a person in a not yet optimally designed sled at h meters in height. Let this sled free fall but user can steer by tilting their body weight in the sled or by optimal sled shape design point it in some horizontal direction where it is wanted to go - in any horizontal direction but once picked fixed. How to calculate horizontal distance d achievable as function of height h. Thus what is f(h) = d. Put another way, imagine a helicopter rises to a height h, but then shuts off all...
View full post »

Similar threads

Uniqueness of Acceleration: Understanding Landau's Mechanics
Replies
39
Views
5K
Equation of Motion: Understand Last Sentence
Replies
4
Views
2K
I What is the acceleration at the contact point between a wheel and surface?
Replies
17
Views
3K
I Coriolis acceleration of a projectile launched at the equator
Replies
4
Views
2K
I Acceleration in Newton's second law
Replies
5
Views
2K
I Why are there 2s -1 independent integrals of motion?
Replies
4
Views
2K
I Energy input\losses for a cyclist accelerating from a standing start
Replies
26
Views
2K
I Help me resolve this apparent paradox
Replies
20
Views
2K
I Using reference frames for derivation of Lagrangian
Replies
25
Views
2K
B The physics of flywheel launchers (like tennis ball shooters)
2
Replies
60
Views
4K

Hot Threads

Recent Insights

Back
Top