Differential Form - Notation Help

[Mistake Not...]

Hi there,

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

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

 

[gleem]

C_ij = ∂f_i/∂q_j
and
C_i = ∂f_i/∂t where f_i is the i th constraint. and q_j is the j ^th coordinate.

 

[lavinia]

Hi there,

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

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. .

 

[stedwards]

I'm quite confused.

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

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