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    Mathematica Taking only the positive sqrt in Mathematica

    As my title says, I need to take only the positive square root of some evaluation. For my calculation, the negative square root is extraneous. What I do is a normalization of a wave function: J = Integrate[Psi[x]^2, {x, 0, a}] sol = Solve[J == 1, A] A /. sol My only problem is those...
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    Intro to Gravitational Simulations

    Hi all, I recently was posting in another thread on how to properly integrate the equations of motion in gravitational simulations. I thought this would be a good opportunity to provide some basic knowledge on simulations, numerical differential equations, and a little bit of programming. I'm...
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    Calculating time derivative of Magnetic force

    Hi all, I ran into a bit of an issue trying to figure out how to properly differentiate the magnetic force due to particle interactions. To be specific, I'm actually looking for the time derivative of acceleration (jerk) due to the magnetic force, but it's essentially the same problem. For...
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    Symplectic Integrators

    Hi all, I'm currently working on some n-body simulations and I'm trying to implement higher order integrators. Currently, I have a Leapfrog and a Hermite integrator (From the student series on The Art of Computational Science). The results I get from Leapfrog are excellent, with respect to...
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    Thought about gravity

    I had a thought before and I'm not sure if this is meaningful to ask or even possible to ask but I'd figure it's worth a shot. Is it meaningful to take the position derivative of acceleration due to gravity? I'd imagine, at least intuitively, this sounds like it's possible. As you move along...
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    Solving differential equations using implicit methods

    Hi all, I'm writing myself a ordinary differential equation solver and I've already implemented several explicit integrators, which were pretty easy for me to do. Now I've decided to work on some implicit methods (for any stiff equations) and I've run into some issues. The most basic one is...
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    Help with Centripetal Force question

    1. Homework Statement A 1000 kg sports car moving at 20 m/s crosses the rounded top of a hill (radius = 100m). Determine (a) the normal force on the car, (b) the normal force on the 70 kg driver, and (c) the car speed at which the normal force is zero. 2. Homework Equations F = ma Fn =...
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    Friction and tension problem

    1. Homework Statement Find the the acceleration, a[/i, and the Tension, [i]T, in the system shown below if (a) m1 = 5 kg and (b) m1 = 2 kg. assume the coefficient of kinetic fricton on the incline plane is µk = 0.1. Other relevant information: Mass 1 is a 5 or 2 kg block on a 30 degree incline...
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