Recent content by Lightf

Homework Statement \phi = 4\arctan{\exp^{m\gamma(x-vt)}} Show \dot{\phi} = -2m\gamma v \sin{\frac{\phi}{2}} Homework Equations The Attempt at a Solution \phi = 4\arctan{\exp^{m\gamma(x-vt)}} \tan{\phi/4} = \exp^{m\gamma(x-vt)} \frac{\dot{\phi}}{4\cos^{2}{\frac{\phi}{4}}} =...

Now I am confused. Should I use Hamiltion's equations then if I use the Hamiltonian? \dot{q}=\frac{dH}{dp}?

Since the L is not explicitly dependent on time \frac{dL}{dt}=0. I cannot see the obvious :( I will try to redo my work with generalised coordinates and see if I makes it clearer.

Homework Statement Consider the following Lagrangian of a relativistic particle moving in a D-dim space and interacting with a central potential field. $$L=-mc^2 \sqrt{1-\frac{v^2}{c^2}} - \frac{\alpha}{r}\exp^{-\beta r}$$ ... Find the velocity v of the particle as a function of p...

Oh can we just give an example, the integers form such a ring but the only invertible elements are 1 and -1. Therefore every non-zero element is not invertible and the question false. Thanks!

Homework Statement Suppose that a commutative ring R, with a unit, has no zero divisors. Does that necessarily imply that every nonzero element of R is invertible? Homework Equations The Attempt at a Solution We have to show that there exists some b in R such that ab = e. Having...

How do you deal with the r outside the square root. When you sub in u you get $$ ∫\frac{du}{(u-\frac{B}{2A})\sqrt{Au^2 +C-\frac{B^2}{4A}}}$$ The (u- B/2A) part throws me off how to solve this. I tried doing it by integration by parts but it just made it more complex. I am also...

Homework Statement Find the deflection angle of the particle if it is scattered by this central field. $$ U = \frac{α - β r - γ r^2}{r^2} $$ Homework Equations Angle of deflection is given by: $$θ = ∫ \frac{Mdr}{r^2\sqrt{2m(E-U) - \frac{M^2}{r^2}}}$$ The Attempt at a Solution...

I'll check my notes again and try again ;) (I'm Fergus - You doing pure maths?)

Homework Statement 3. (a) Show that every quaternion z of length 1 can be written in the form z = cos(\alpha/2) + sin(\alpha/2)n, for some number α and some vector n, |n| = 1. (b) Consider two rotations of the 3d space: the rotation R_1 through \alpha_1 around the vector n_1 and the rotation...

This is how i did it : Let : z = a + ib + jc + kd Then sub that into the formula : \overline{z} = \frac{1}{2}(-z-izi - jzj - kzk) And just carefully multiply it out... -iz = -ia - i^{2}b - ijc - ikd -iz =-ia + b -kc +jd -izi = -i^{2}a+ib-kic + jid -izi=a+ib-jc-kd And repeat...

So eae0 is 1110101011100000 but the first 1 just means its a minus number so its -27360

So the answer would be : 7fff - eae0 = 6ae1 6ae1 - 8000 = -151f which is -5497 in dec. Is that the correct way of doing it? Thanks for the help.

Homework Statement The question is : Converting to short int, calculate 30064 + 30064 as short integers. Convert the answer to decimal ( the answer will be negative ). Homework Equations None. The Attempt at a Solution I converted 30064 to hex getting 7570. I then added...

I worked it out now. Let : z = a + ib + jc + kd (and z bar = a - ib - jc -kd ) Then just multiply it out.