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The simplest way to look at this is to consider separately the horizontal and vertical velocity/position. For a projectile launched at angle $\theta$ and velocity $v$, the components are: Horizontal velocity $$v_h = v\cos\theta$$ Vertical velocity $$v_v = v\sin\theta$$ The position at time $t$ is then given by $$(x, y) = (v_h\cdot t, v_v \cdot t - ...


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The diffusion is caused by collisions between the molecules due to the random thermal motion of each molecule. So you have a blob of oxygen in a box of nitrogen then they are all moving with a random velocity from the Maxwell velocity distribution. When two molecules collide, they change velocity and so they change both speed/direction. They then collide ...


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Diffusion is one of several entropic phenomena the average effect of which can be described as a purely Newtonian phenomenon. This is done via the introduction of an entropic force. For diffusion the entropic force takes the shape of a repulsive radial force directed away from the starting position of the diffusion process: $$F_r=\frac{2kT}{r}$$ Here, $k$ ...


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It sounds like you're trying to solve the Langevin Equation. This is a model of Brownian motion where the particle experiences stochastic kicks at discrete time intervals. Your force, in this case, is a random variable you draw from a distribution each time step (instead of being given by an explicit formula). For the simplest case, the "kicks" are ...


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The method you are using here is Euler-Cromer. It only really works for sytems with two variables (although I guess it could be modified for systems with any even number of variables - e.g. find $x, y, z$ then $vx, vy, vz$). There is a more accurate method, which is more general, but more complicated to program. This is the 4th order Runge Kutta (RK) ...


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Molecular simulation is certainly used in the field of astrobiology. For example, here's a quote from a NASA technical report specifically on Molecular Simulations in Astrobiology: We use computer simulations to address the following, questions about these proteins: (1) How do small proteins (peptides) organize themselves into ordered structures at ...


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Now I am stuck, trying to find the velocity and position of two bodies (ignoring all the others) after one time-step with given mass, start position and velocity. You get the final velocity at impact $v$ with $$v=\sqrt{\int_{r_1}^{r_2} \left(\frac{2 G M}{r^2}+\frac{v_0^2}{r_1-r_2}\right) \, \text{d}r}$$ Where $r_2$ is the initial distance and $r_1$ ...


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For two bodies this is relatively easy as the equations of motion describe a conic (an ellipse for a closed orbit, a hyperbola for an "open" orbit). You can use the vis viva equation to get the parameters of the orbit (semi major axis etc) from the given initial conditions, and the rest follows. For an ellipse, you can also express the position as a ...


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Rather than leave these as comments, I guess I should answer it since this has come up before. A 2D simulation does not mean there is no third dimension. Rather, it means we are saying there is no variation in the third dimension such that $\frac{\partial}{\partial z} = 0$. But that depth direction still exists and we typically just call it a "unit depth" ...



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