# Tag Info

1 vote
Accepted

### Formula for predicting next position does not include maximum velocity. Is there a formula that does?

The original formula you gave is obtained by integrating the velocity: $x(t) = x_0 + \int_{0}^{t} v(t) dt = x_0 + \int_{0}^{t} (v_0 + at) dt = x_0 + v_0 t + \frac{1}{2} at^2$ Where we computed $v(t)$ ...
• 920

• 87.6k
1 vote
Accepted

### Following/Seeking a Moving Position with Velocity & Sin/Cos

It doesn't specify what language you are using, but atan2 almost universally takes the $y$ coordinate first and the $x$ coordinate second, and then why are you ...
• 10.4k
1 vote
Accepted

• 224k
Accepted

### Why do physicists label irreducible representations of su(2) with half integers?

To my mind, the explanation is at the level of Lie groups, not Lie algebras, since the Lie algebras preserve slightly less information than the Lie groups. Here, while $su(2)\to so(3)$ is an ...
• 48.1k
1 vote
Accepted

### Initial-value problem with a forcing function that has step discontinuity

I thought that it might be instructive to present an alternative approach that recasts the problem using a nascent Dirac Delta [1]. To that end we proceed. Suppose $x_n(t)$ satisifies the ...
• 168k
1 vote
Accepted

• 23.2k

### Collision time of 2 circles with friction

Your equation is correct, the time where the objects collide is the smallest solution of the equation. Unless this is a special case, that equation can't be simplified any better since if you're able ...
• 94

• 66

### How does the pushforward of the inverse metric relate to the inverse of the pullback metric for an embedding?

As pointed out in the comments, the subspace projection in $TM$ needs to account for the metric $g$. I have put together a proof on matrix level to see how the pieces come together: If we obtain the ...
1 vote

### The vector A whose magnitude is 1.72 units makes equal angles with the coordinates axes. Find Ax,Ay,Az

The results are different because you took the liberty to claim that the angle was $45^\circ$. Whereas the angle must be $\cos \frac{-1}{\sqrt3}\simeq54^\circ$ (approx). Which can be found by the ...
• 11

• 3,651
1 vote

### What does the "3" in $d^3x_1d^3p_1\ldots d^3x_Nd^3p_N$ mean here?

The explanation may be found on page 2 of the document. Here is an image: It's the same number as the 6N here: You have $N$ particles with 3 position and 3 momentum values each.
• 10.4k

### What does the "3" in $d^3x_1d^3p_1\ldots d^3x_Nd^3p_N$ mean here?

It's just an index indicating that you are considering a volume (3D) integral. Each of the $x_j$ and $p_j$ is a vector with $3$ components.
• 8,172
Often in physics we want the real solutions to an equation which, due to linearity, has the following property: if $x$ is an in general complex solution, so are $x^\ast$ and the real-valued linear ...