Differential Form - Notation Help

In summary, the conversation discusses the notation for a differential form in the context of Holonomic constraints. The equation on the Wikipedia page is given as Cij = ∂fi/∂qj and Ci = ∂fi/∂t, where fi is the i th constraint and qj is the j th coordinate. The question is posed for an explanation of the notation and any helpful links or documents. The response includes an interpretation of the notation as small increments and an explanation of a differential 1 form. There is also a question about the presence of lower indices on the q coordinate differentials and the expectation of an equal number of indices on c.
  • #1
Mistake Not...
2
0
Hi there,

I was reading up on Holonomic constraints and came across this equation on the Wikipedia page:

fa14f9c440da57168334ebf30c88cf09.png


The page says it is a differential form. Can anyone explain the notation for me or provide a link or two to documents or pages which explain this notation?

Thank you very much,
Geoff
 
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  • #2
Cij = ∂fi/∂qj
and
Ci = ∂fi/∂t where fi is the i th constraint. and qj is the j th coordinate.
 
  • Like
Likes Mistake Not...
  • #3
Mistake Not... said:
Hi there,

I was reading up on Holonomic constraints and came across this equation on the Wikipedia page:

fa14f9c440da57168334ebf30c88cf09.png


The page says it is a differential form. Can anyone explain the notation for me or provide a link or two to documents or pages which explain this notation?

Thank you very much,
Geoff

You can interpret the dhqs and dt as small increments in the q's and in t.

Formally a differential 1 form is a linear function on tangent vectors that varies smoothly from one tangent space to the next. .
 
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Likes Mistake Not...
  • #4
I'm quite confused.

fa14f9c440da57168334ebf30c88cf09.png


Why are there lower indices on the ##q^i##coordinate differentials?

I would also expect to see an equal number of indeces on ##c##.
 
Last edited:

Related to Differential Form - Notation Help

1. What is differential form notation?

Differential form notation is a mathematical notation used to express concepts related to multivariable calculus and differential geometry. It is a way of representing multivariable functions, vectors, and other mathematical objects in a concise and elegant manner.

2. How is differential form notation different from traditional notation?

Traditional notation typically uses indices and coordinates to represent mathematical objects, whereas differential form notation uses symbols and operations such as the exterior derivative and wedge product. This makes differential form notation more compact and easier to manipulate.

3. What are the advantages of using differential form notation?

Differential form notation allows for a more concise and elegant representation of mathematical concepts, making it easier to understand and work with. It also has a more geometric interpretation, making it useful for applications in fields such as physics and engineering.

4. How is differential form notation used in physics and engineering?

Differential form notation is commonly used in physics and engineering to express concepts such as vector fields, flux, and work. It allows for a more intuitive and geometric understanding of these concepts, making it easier to apply them to real-world problems.

5. Are there any resources available for learning differential form notation?

Yes, there are many resources available for learning differential form notation, including textbooks, online tutorials, and video lectures. It is also helpful to have a strong understanding of multivariable calculus and linear algebra before diving into differential form notation.

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