多粒子問題二：三個粒子在電磁疊加場的運動仿真

序言

過了好幾天，終於有時間把這個寫出來啦！！！
接着上一篇文章繼續寫。

Precondition

the situation is special,the initial condition is shown in the following figure

Part2

Motion Of Three Particles

E = 0.3;    %決定粒子往x軸運動的情況
B = 0.65;   %決定粒子往y軸旋轉的情況
kappa = 9.6;
const = 0.125;
dt = 0.01;
x1 = zeros(1,100);
y1 = zeros(1,100);
z1 = zeros(1,100);
x2 = zeros(1,100);
y2 = zeros(1,100);
z2 = zeros(1,100);
x3 = zeros(1,100);
y3 = zeros(1,100);
z3 = zeros(1,100);
vx1 = zeros(1,100);
vy1 = zeros(1,100);
vz1 = zeros(1,100);
vx2 = zeros(1,100);
vy2 = zeros(1,100);
vz2 = zeros(1,100);
vx3 = zeros(1,100);
vy3 = zeros(1,100);
vz3 = zeros(1,100);
t = zeros(1,100);
x2(1) = 1;
y3(1) = 1;
i = 1;
rrr12 = zeros(1,100);
rrr13 = zeros(1,100);
rrr23 = zeros(1,100);
rrr12(1) = 1;
rrr13(1) = 1;
rrr23(1) = 2^0.5;
while i<round(10/dt)
    vx1(i+1) = vx1(i) + dt*kappa*(E+const*((x1(i)-x2(i))/rrr12(i) + (x1(i)-x3(i))/rrr13(i))-B*vz1(i));
    vy1(i+1) = vy1(i) + dt*kappa*const*((y1(i)-y2(i))/rrr12(i) + (y1(i)-y3(i))/rrr13(i));
    vz1(i+1) = vz1(i) + dt*kappa*(const*((z1(i)-z2(i))/rrr12(i) + (z1(i)-z3(i))/rrr13(i))+B*vx1(i));
    x1(i+1) = x1(i) + dt*vx1(i+1);
    y1(i+1) = y1(i) + dt*vy1(i+1);
    z1(i+1) = z1(i) + dt*vz1(i+1);
    vx2(i+1) = vx2(i) + dt*kappa*(E+const*((x2(i)-x1(i))/rrr12(i) + (x2(i)-x3(i))/rrr13(i))-B*vz2(i));
    vy2(i+1) = vy2(i) + dt*kappa*const*((y2(i)-y1(i))/rrr12(i) + (y2(i)-y3(i))/rrr13(i));
    vz2(i+1) = vz2(i) + dt*kappa*(const*((z2(i)-z1(i))/rrr12(i) + (z2(i)-z3(i))/rrr13(i))+B*vx2(i));
    x2(i+1) = x2(i) + dt*vx2(i+1);
    y2(i+1) = y2(i) + dt*vy2(i+1);
    z2(i+1) = z2(i) + dt*vz2(i+1);  
    vx3(i+1) = vx3(i) + dt*kappa*(E+const*((x3(i)-x1(i))/rrr12(i) + (x3(i)-x2(i))/rrr13(i))-B*vz3(i));
    vy3(i+1) = vy3(i) + dt*kappa*const*((y3(i)-y1(i))/rrr12(i) + (y3(i)-y2(i))/rrr13(i));
    vz3(i+1) = vz3(i) + dt*kappa*(const*((z3(i)-z1(i))/rrr12(i) + (z3(i)-z2(i))/rrr13(i))+B*vx3(i));
    x3(i+1) = x3(i) + dt*vx3(i+1);
    y3(i+1) = y3(i) + dt*vy3(i+1);
    z3(i+1) = z3(i) + dt*vz3(i+1);
    rrr12(i+1) = ((x1(i+1)-x2(i+1))^2+(y1(i+1)-y2(i+1))^2+(z1(i+1)-z2(i+1))^2)^1.5;
    rrr13(i+1) = ((x1(i+1)-x3(i+1))^2+(y1(i+1)-y3(i+1))^2+(z1(i+1)-z3(i+1))^2)^1.5;
    rrr23(i+1) = ((x3(i+1)-x2(i+1))^2+(y3(i+1)-y2(i+1))^2+(z3(i+1)-z2(i+1))^2)^1.5;
    t(i+1) = t(i) + dt;
    i = i + 1;
end

粒子的運動軌跡如下圖

說明一下此圖僅描述了粒子一的運動情況

總結

有了初步建模的方法，以後會再接再勵模擬更復雜更有趣的系統，爲興趣而活，模擬全世界！
還有數據分析也是自己的一個發展方向。日後也要多家練習。