Understanding the Dot Product of Derivatives

In summary, The conversation is about a confusion regarding a formula in a Dynamics lecture. The lecturer mentioned that dr/dt dotted with d2r/dt2 equals (1/2)(d/dt(dr/dt dotted with dr/dt)), which the person is having trouble understanding. They speculate that it has something to do with the product rule and apologize for their notation. Another person suggests evaluating \frac{dr}{dt}\cdot\frac{dr}{dt} using the product rule.
  • #1
teeeeee
14
0
Hi,
Im having trouble understanding something in one of my Dynamics lectures.
The lecturer said that:

dr/dt dotted with d2r/dt2 (where r is a vector)

equals: (1/2)(d/dt(dr/dt dotted with dr/dt))...

I just can't get this result. I know it has something to do with the product rule.

Thanks for your help, and sorry for the crudity of my notation :-p

teeeeee
 
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  • #2
teeeeee said:
I know it has something to do with the product rule.

It does. Have you tried evaluating [tex]\frac{dr}{dt}\cdot\frac{dr}{dt}[/tex] using the product rule? What do you get?
 
  • #3
I believe Cristo meant evaluating
[tex]\frac{d}{dt}\left(\frac{dr}{dt}\cdot\frac{dr}{dt}\right)[/tex]
 

FAQ: Understanding the Dot Product of Derivatives

What is the dot product of derivatives?

The dot product of derivatives is a mathematical operation that calculates the scalar product of two vectors. It involves multiplying the magnitudes of the two vectors and the cosine of the angle between them.

How is the dot product of derivatives used in science?

The dot product of derivatives is used in various fields of science, such as physics, engineering, and computer science. It is especially useful in calculating the work done by a force and in determining the direction of a vector.

What is the formula for calculating the dot product of derivatives?

The formula for calculating the dot product of derivatives is:
a · b = |a| * |b| * cos(θ)
where a and b are vectors, |a| and |b| are the magnitudes of the vectors, and θ is the angle between them.

What is the significance of the angle between two vectors in the dot product of derivatives?

The angle between two vectors in the dot product of derivatives determines the direction of the resulting vector. If the angle is 0 degrees, the resulting vector will have the same direction as the original two vectors. If the angle is 90 degrees, the resulting vector will be perpendicular to both vectors.

Can the dot product of derivatives be negative?

Yes, the dot product of derivatives can be negative. This occurs when the angle between the two vectors is greater than 90 degrees, resulting in a negative value for the cosine term in the formula. This indicates that the vectors are pointing in opposite directions.

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