All Questions
5 questions with no upvoted or accepted answers
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Vector Derivative: General Case
From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector".
In this section, towards the end, ...
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Does the proper four-acceleration $A^{\mu} = (0,0)?$
Let the proper four-position vector $x^{\mu}(\tau) = (0, \tau)$. Differentiating this successively wrt $\tau$ I get the four-velocity $u^{\mu}(\tau) = (0, 1)$ and then the four-acceleration $A^{\mu}(\...
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Are terms tangential acceleration and normal acceleration only used for instantaneous velocity?
Are terms tangential acceleration and normal acceleration only used
for instantaneous velocity?
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1/velocity for higher dimensions
I have a somewhat basic question. I am sorry if it trivial.
Denote the velocity by $v=\frac{dx}{dt}$ suppose that $x \in \mathbb{R}^n$ and I want to parametrize $t$ in $x$ and compute $\frac{dt}{dx}$. ...
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Product rule for 4-vectors and derivation of 4-force form
In deriving the form for the 4-force in special relativity, we begin with
$$\frac{d}{d\tau}p^{\alpha}=m\frac{d}{d\tau}u^{\alpha}=f^\alpha$$
where $\tau$ is the proper time, m is rest mass.
Since $...
