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This paper introduced the so-called $m_h^\mathrm{max}$ scenario which maximizes the highest possible value for $m_h$ for each value of $\tan \beta$ (and for a fixed value of $M_\mathrm{SUSY}$, note that the top mass has decreased a bit since the paper was written). Looking at Figure 4, it looks (at least with their choices of other parameters), that the ...


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The distance is a function of the angle. I am pretty sure you won't be able to obtain the inverse function analytically, not taking into account air resistance, so you should solve the relevant equation numerically, using one of the well-known methods, such as dichotomy or the secant method.


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A couple things, first you are not discussing air resistance correctly. The drag depends on the current velocity, which is a dynamical quantity, not just on the muzzle velocity. You need to use the current velocity at any step of the calculation. Second, in broad terms, you can think of the problem you face as one of root finding. You have some function ...


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For Mathematica the best I know is RGTC. I Used it a long time ago (briefly) for a calculation in IIA SUGRA in 10 dimensions. It calculate gravitational tensors, manages differential forms (also Lie algebra valued ones), calculates Hodge dualities, etc. Personal comment: If you are more intrepid (and FLOSS lover), there is a software called SAGE, which ...


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There are the EMS, an add-in to Solidowrks, so you can simulate in 3D: (payed). Others: Amperes Quickfield MagNet Open source: MaxFEM


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Even though your integration method seems wrong, like David Hammen pointed out, the results look do not look wrong. The problem rely lies with the way you define your ellipse. Your definition for the semi-major axis, $a$, and eccentricity, $e$, are correct. The way you define the semi-minor axis, $b$, probably is not, which is defined as: $$ b = a \sqrt{1 - ...


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Here's your key error: var dx = Add(Mul(gv , dt*dt) , Mul(o.v, dt)); // position changes In math, that's $\Delta \vec x = \vec g \Delta t^2 + \vec v \Delta t$. That's incorrect. Assuming a constant acceleration $\vec g$, the change in position over some time interval $\Delta t$ is given by $\Delta x = \frac 1 2 \vec g \Delta t^2 + \vec v \Delta t$. That ...


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I) One mathematical problem is that the function $$\tag{1} f(q)~:=~ \frac{q\sin(rq)}{q^2+u^2}, \qquad q,r,u~>~0, $$ is not integrable $f\notin {\cal L}^{1}(\mathbb{R}_{+})$, because the integral over the absolute value of the integrand is infinite: $$\tag{2} \int_{\mathbb{R}_{+}} \! dq~|f(q)| ~=~\infty.$$ However it is still possible to define the ...



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