The angular velocity vector of a rigid body is defined as $\vec{\omega}=\frac{\vec{r}\times\vec{v}}{|\vec{r}|^2}$. But that's not how most people intuitively think about angular velocity.
Euler's theorem of rotation states that any rigid body motion with one point fixed is equivalent to a rotat...
I am asked to solve the following ODE involving constants $\alpha, L, V_0 > 0$ and $E < 0$:
$$-\psi'' - \alpha V_0\psi\cdot [\delta(x)+\delta(x-L)] = \alpha E\psi.$$
In particular, we want solutions $\psi:\mathbb{R}\to \mathbb{C}$ that are:
Continuous
$L^2$
We are given that the solutions l...
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group.
The theorem is named after Leonhard Euler, who proved it in 1775 by an elementary geometric argument. The axis of rotation is known as an Euler axis, typically represented by a unit vector
...
Is the following true?
$G$ is a torsion free abelian group of rank $>n$.
Let $S$ be be a subgroup of $G$ generated by $s_1,s_2, \cdots ,s_n$.
(1) If $m_1s_1+m_2s_2+ ...+m_ns_n$ is linearly independent modulo $p$ for every prime $p$, then $S$ is linearly independent. That is, if $m_1s_1+m_...
In computer science, the iterated logarithm of n, written log* n (usually read "log star"), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1. The simplest formal definition is the result of this recursive function:
log
∗
n
:=
{
0
if
...
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