How to show the Hamiltonian is conserved
I have the langrangian $L = \frac 1 2m((1+4r^2)r’^2) + \frac 1 2 mr^2 θ’^2 -mgr^2 $ I worked out theHamiltonian and 4 Hamiltonian equations and got $\frac...
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I have the langrangian $L = \frac 1 2m((1+4r^2)r’^2) + \frac 1 2 mr^2 θ’^2 -mgr^2 $ I worked out theHamiltonian and 4 Hamiltonian equations and got $\frac...
Can someone please help me in figuring out how all fields are integral domains but not all ID are fields? My course assumes IDs to be commutative with uni...
How does one know that a number field $K$ has a maximal abelian extension (unique up to isomorphism) $K^{\text{ab}}$? I've read proofs involving Zorn...
I want to understand how to convert from Cartesian coordinates to spherical coordinates. I have the following definitions: \begin{align} x & =r\sin\th...
What are the different methods for solving a linear equation with integral Solutions? Which one is preferred over other? What is the best method? For exam...
Here's an equation from a text book for computing a unit vector: $$\hat v = \frac{\overline v}{ \sqrt{ \sum ^n _{i=1} (\overline v_i)^2 } }$$ Now I m...
This seems like such an elemental thing to me, but I don't want to assume it's always true, since there could be an exception. Also, without kno...
In the function topic of "function combinations" or "function algebra", for the basic arithmetic operations of the following: 1) f + g 2) f - g 3) f * g 4...
a three-character password consists of 2 different digits between 0 and 9 inclusive. and 1 letter of the English alphabet. the letter must appear as first...
What does the letter U mean in the following expression: $$ \bigcup_{\alpha} A_\alpha \;? $$ It doesn't look like logical OR. Link to original screen...