牛顿摇篮:与钟摆的弹性碰撞

在我的程序中，我有 5 个摆动的钟摆，它们都由滑块值一次修改。这些值被绘制到从并传递到类钟摆上。要更改值，将运行更新按钮，并且有一个默认选项来使用有效的设置。这些值也通过一些简单的标签显示在屏幕上。零按钮将所有值（长度除外）设置为零。

现在我的下一个任务是让钟摆"逼真"碰撞，并重现牛顿摇篮式效果。我已经研究了粒子上的弹性碰撞解决方案，例如，这里有一个很好的例子：球对球碰撞 - 检测和处理

我也在这里研究了它背后的原始物理学，但我的大脑无法掌握事物的原始物理学方面。

所以我想知道是否有人可以帮助我弄清楚碰撞的理论。
我目前的想法是，当坐标相遇时，速度将简单地改变极性，例如在相对的钟摆中+10到-10。我在这里说得对吗？

这是我的钟摆课：

class Pendulum 
{
    //all public static so they are actually global (can be used between classes and not just global to this class).
    public static int length = 10;//length of arm /** can't be less than 0 or will break.
    public static double angle = 0; //pendulums arm angle
    public static double aAcc = 0.00; //Angle acceleration
    public static double aVel = 0.00; //anglular velocity
    public static double damping = 0.000; //friction //friction
    public static double gravity = 0.0; //make gravity a constant
    int originX = 0;
    int originY = 0; //allways 0
    int bobX; // = frmWidth / 2;
    int bobY; // = (int)length; Drawn in pendulm as don't really need to be global. Are currently for flexibilty.
    Timer timer; //global for flexibility
    public Pendulum(int frmWidth, int frmHeight)
    {
        timer = new Timer() { Interval = 30 };
        timer.Tick += delegate(object sender, EventArgs e)
        {
            //-----------------drawing variables------------------------------//
            originX = frmWidth / 2;
            originY = 0;
            //to be relative to origin we go:
            bobX = originX + (int)(Math.Sin(angle) * length);
            bobY = originY + (int)(Math.Cos(angle) * length);
            //gravity
            aAcc = (-1 * gravity / length) * Math.Sin(angle); //calculate acceleration
            aVel += aAcc;//increment velcocity
            angle += aVel;//incrment angle
            aVel *= damping;//friction action, pendulum eventually 0's
        };
        timer.Start();
    }
    public void DrawPendulum(Graphics g) 
    {
            g.DrawLine(Pens.Black, originX, originY, bobX, bobY);
            g.FillEllipse(Brushes.Red, bobX - 8, bobY, 20, 20); //-8 to make it look more central!
    }
}

这是表单代码：

public partial class frmPendulum : Form
{
    private Timer timer;
    private Pendulum p1 = null;
    private Pendulum p2 = null;
    private Pendulum p3 = null;
    private Pendulum p4 = null;
    private Pendulum p5 = null;

    public frmPendulum()
    {
        InitializeComponent();
        this.Shown += new EventHandler(frmPendulum_Shown);
        this.Paint += new PaintEventHandler(frmPendulum_Paint);
    }
    void frmPendulum_Shown(object sender, EventArgs e)
    {
        p1 = new Pendulum(this.ClientRectangle.Width, this.ClientRectangle.Height);
        p2 = new Pendulum(this.ClientRectangle.Width + 40, this.ClientRectangle.Height);
        p3 = new Pendulum(this.ClientRectangle.Width - 40, this.ClientRectangle.Height);
        p4 = new Pendulum(this.ClientRectangle.Width - 80, this.ClientRectangle.Height);
        p5 = new Pendulum(this.ClientRectangle.Width + 80, this.ClientRectangle.Height);
        timer = new Timer() { Interval = 100 };
        timer.Tick += delegate(object s2, EventArgs e2)
        {
                this.Refresh();
                Value.Text = string.Format("Length: " + Pendulum.length + "{0}Angle: " + Pendulum.angle + "{0}Acc: " + Pendulum.aAcc + "{0}Vel: " + Pendulum.aVel + "{0}Damping: " + Pendulum.damping + "{0}Gravity: " + Pendulum.gravity, Environment.NewLine);
                value2.Text = string.Format("Length: " + tbrLength.Value + "{0}Angle: " + ((double)tbrAngle.Value) / 100.0 + "{0}Vel: " + ((double)tbrAVel.Value) / 100.0 + "{0}Damping: " + ((double)tbrDamp.Value) / 100.0 + "{0}Gravity: " + ((double)tbrGrav.Value) / 100.0, Environment.NewLine);
        };
        timer.Start();
    }
    void frmPendulum_Paint(object sender, PaintEventArgs e)
    {
        switch (tbrNoOfPend.Value)
        {
            case 1:
                if (p1 != null) //if used because the Paint() event could occur BEFORE "p1"etc. has been instantiated.
                {
                    p1.DrawPendulum(e.Graphics);
                }
                break;
            case 2:
                if (p2 != null)
                {
                    p2.DrawPendulum(e.Graphics);
                }
                goto case 1;
            case 3:
                if (p3 != null)
                {
                    p3.DrawPendulum(e.Graphics);
                }
                goto case 2;
            case 4:
                if (p4 != null)
                {
                    p4.DrawPendulum(e.Graphics);
                }
                goto case 3;
            case 5:
                if (p5 != null)
                {
                    p5.DrawPendulum(e.Graphics);
                }
                goto case 4;
            default:
                break;
        }
    }

    private void btnDefault_Click(object sender, EventArgs e)
    {
        //sets values to a good calibration by default.
        Pendulum.length = 50;
        Pendulum.angle = Math.PI / 2; //pendulums arm angle
        Pendulum.aAcc = 0.00; //Angle acceleration
        Pendulum.aVel = 0.00; //anglular velocity
        Pendulum.damping = 0.995; //friction //friction
        Pendulum.gravity = 0.4; //make gravity a constant
        UpdateSliders();
    }
    private void UpdateValues()
    {
        /** The trackbars only use integer values so to increment in decimals certain values have to be divided by 100 so they are correct in the simulation.
         * For example is I want the gravity to be 0.4 my track bars value will have to be 40 / 100 = 0.40 
         * Another example will be angle that will go from -3 to 3 incrementing in decimals we go from -300 to 300 /100 = 3 **/
        Pendulum.length = tbrLength.Value; //length is ok as it is an integer
        Pendulum.angle = ((double)tbrAngle.Value) / 100.0; //both numerator and denominator must be of the same type.
       // acceleration is calculated so isn't sent
        Pendulum.aVel = ((double)tbrAVel.Value) / 100.0; 
        Pendulum.damping = ((double)tbrDamp.Value) / 100.0; 
        Pendulum.gravity = ((double)tbrGrav.Value) / 100.0; 
    }
    private void UpdateSliders()
    {
        tbrLength.Value = Pendulum.length;
        tbrAngle.Value = (int)(Pendulum.angle * 100.0); //pendulums arm angle
        //tbrAAcc.Value = (int) Pendulum.aAcc; //Removed acceleration as it is re-calculated anyway.
        tbrAVel.Value = (int)(Pendulum.aVel* 100.0); //anglular velocity
        tbrDamp.Value = (int)(Pendulum.damping * 100.0); //friction //friction
        tbrGrav.Value = (int)(Pendulum.gravity * 100.0); //make gravity a constant
    }
    private void btnUpdateValues_Click(object sender, EventArgs e)
    {
        UpdateValues();
        //this.Shown += new EventHandler(frmPendulum_Shown);
        //this.Paint += new PaintEventHandler(frmPendulum_Paint);
    }
    private void button1_Click(object sender, EventArgs e)
    {
        //zero's everything except length.
        Pendulum.angle = 0; //pendulums arm angle
        Pendulum.aAcc = 0.00; //Angle acceleration
        Pendulum.aVel = 0.00; //anglular velocity
        Pendulum.damping = 0; //friction //friction
        Pendulum.gravity = 0; //make gravity a constant
        UpdateSliders();
    }
}