- #1
kent davidge
- 933
- 56
Which ways are available to know how two frames are connected? I mean, to know how they are related to one another?
How to See How Two Frames are Connected?
- I
- Thread starter kent davidge
- Start date
-
- Tags
- Frames
In summary: I don't know, I was just thinking about this, I have no explicit case in mind.In summary, two frames are connected if there is a coordinate transformation that specifies the relationship between the frames.
- #2
- 19,048
- 14,674
Do you mean frames of reference? If so, they are NOT "connected". Objects can be described from the point of view of either FOR but I don't see that that "connects" the frames.
In other words, you don't relate frames to frames, you relate objects to frames.
In other words, you don't relate frames to frames, you relate objects to frames.
- #3
Nugatory
Mentor
- 15,131
- 9,899
There will be a coordinate transformation between the coordinates used in one frame and the coordinates used in the other. That transformation completely specifies the relationship between the frames.kent davidge said:
- #4
strangerep
Science Advisor
- 3,765
- 2,212
... unless one (or both) frames are nonholonomic.Nugatory said:
@kent davidge : Your question could be answered more helpfully if you gave a specific example of 2 such frames.
- #5
kent davidge
- 933
- 56
[Mentors' note: This post was edited to avoid an unnecessary flame war]
What if the coordinate transform is masked? For example, what if the two frames are simply two inertial frames connected by a Lorentz transformation, but they were written in a weird fashion. I suspect there should exist a coordinate independent way of actually finding this out.Nugatory said:
I don't know, I was just thinking about this, I have no explicit case in mind.strangerep said:
Last edited by a moderator:
- #6
Nugatory
Mentor
- 15,131
- 9,899
A frame is a convention for assigning coordinates to events. I'm finding it difficult to imagine how any relationship between two such conventions could be related in a coordinate-independent way.kent davidge said:
- #7
PeterDonis
Mentor
- 47,525
- 23,789
kent davidge said:
What does this mean?
kent davidge said:
A Lorentz transformation is a coordinate transformation between inertial coordinates. If the coordinates are "written in a weird fashion" you can't use a Lorentz transformation anyway.
- #8
PeterDonis
Mentor
- 47,525
- 23,789
kent davidge said:
Then I think you need to think harder and come up with a specific example. At this point I don't understand what you mean by "how two frames are connected", and having a specific example of two frames and you describing what connection you are talking about would help a lot.
- #9
- 10,342
- 1,518
As I recall, a "frame" could mean a lot of things. One popular definition, though not the only one, is that a frame assigns a set of basis vectors to any point in the manifold.
But sometimes a frame is used as another name for a coordinate system.
"Connections" are also used for Christoffel symbols, which can be regarded as the map from a set of basis vectors at the tangent space of one point in a manifold to the set of basis vectors in the tangent space of a different, nearby, point in the manifold.
So a bit more explanation of what you're looking for exactly would be really helpful.
But sometimes a frame is used as another name for a coordinate system.
"Connections" are also used for Christoffel symbols, which can be regarded as the map from a set of basis vectors at the tangent space of one point in a manifold to the set of basis vectors in the tangent space of a different, nearby, point in the manifold.
So a bit more explanation of what you're looking for exactly would be really helpful.
FAQ: How to See How Two Frames are Connected?
How do I determine the connection between two frames?
To see how two frames are connected, you can use a variety of methods such as visual inspection, mathematical analysis, or experimental testing. It may also be helpful to consult previous research or consult with other experts in the field.
Can I use software to see the connection between two frames?
Yes, there are various software programs available that can help you visualize and analyze the connection between two frames. Some examples include finite element analysis software, motion analysis software, and structural analysis software.
What factors should I consider when examining the connection between two frames?
Some important factors to consider when examining the connection between two frames include the type of connection (e.g. welded, bolted, pinned), the material properties of the frames, the load and forces acting on the frames, and the overall design and geometry of the frames.
How can I ensure the connection between two frames is strong and stable?
To ensure a strong and stable connection between two frames, it is important to carefully design and engineer the connection based on the specific requirements and load conditions. This may involve using appropriate materials, following industry standards and codes, and conducting thorough testing and analysis.
Are there any common mistakes to avoid when examining the connection between two frames?
Some common mistakes to avoid when examining the connection between two frames include overlooking important factors, using incorrect assumptions or calculations, and not considering the potential failure modes of the connection. It is also important to carefully review and double-check all data and results to ensure accuracy.