3BodyProblem/BodyMaths.java at Final · watem/3BodyProblem · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
/**
* This logic class contains all of the equations for three body problems involving gravity or electrostatics.
* This class also contains the formulae for gravitational Lagrange points.
* @author Matthew Williams, Yulia Kosharych
* @version 2018-05-16
**/
public class BodyMaths {


  // import constants
  public static final double G = SolarBody.G;


  /**
  * This method calculates the acceleration that one body causes on another due to gravity
  * @param obj[][] double               these are the positions of the object that the acceleration is calculated on
  * @param body[][] double              these are the positions of the body that causes the gravitional acceleration on the object
  * @param massBody double              this is the mass of the body that causes the acceleration
  * @param i int                        this is the current timestep
  * @param axis int                     this is the axis that is currently being calculated (0=x, y=1)
  * @return acceleration double         this is the value of acceleration along the selected axis
  * @version 2018-04-25
  **/
  public static double gravityAccel(double obj[][], double body[][], double massBody, int i, int axis){
    double acceleration;
    acceleration = -G*massBody*(obj[axis][i]-body[axis][i])/Math.pow(radius(obj, body, i), 3);
    return acceleration;
  }//dualBodyAccel()


  /**
  * This method calculates the magnitude of a two dimensional vector
  * @param x double         this is the x component of the vector
  * @param y double         this is the y component of the vector
  * @return norm double     this is the magnitude of the vector
  * @version 2018-04-25
  **/
  public static double norm(double x, double y) {
    double norm = Math.sqrt(x*x+y*y);
    return norm;
  }//norm()

  /**
  * This method calculates the distance between two bodies at a specific timestep
  * @param body1[][] double       these are the positions of first body
  * @param body2[][] double       these are the positions of second body
  * @param i int                  this is the current timestep
  * @return norm                  this is the magnitude of the distance between the two bodies
  * @version 2018-04-25
  **/
  public static double radius(double body1[][], double body2[][], int i) {
    double x = body1[0][i] - body2[0][i];
    double y = body1[1][i] - body2[1][i];
    return norm(x, y);
  }//radius()

  /**
  * This method updates the velcity and positions for a timestep based on the acceleration
  * @param obj[][][] double       these are the position, velocity, acceleration vectors for a body
  * @param dt double              this is the timestep length
  * @param i int                  this is the current timestep
  * @version 2018-05-16
  **/
  public static void updateBody(double obj[][][], double dt, int i){
    // velocity = vI + a*dt
    obj[1][0][0]+=obj[2][0][i]*dt;
    obj[1][1][0]+=obj[2][1][i]*dt;
    // position = xI + v*dt
    obj[0][0][i]=obj[0][0][i-1]+obj[1][0][0]*dt;
    obj[0][1][i]=obj[0][1][i-1]+obj[1][1][0]*dt;
  }//updateBody()


  // Lagrange points
  /**
  * These methods (L1 to L3) give the distances to the legrange points. m1>m2
  *
  * @param distance double    this is the distance between the major bodies
  * @param m1       double    this is the mass of the body that is much larger than m2
  * @param m2       double    this is the mass of the body that is much smaller than m1
  *
  * @return r       double    for L1 this is the distance from the smaller object towards the larger object
  *                           for L2 this is the distance from the smaller object away from the larger object
  *                           for L3 this is the distance from the larger object away from the smaller object
  * @version 2018-05-08
  **/
  public static double L1(double distance, double m1, double m2){
    double r = Math.abs(distance)*Math.pow(m2/(3*m1), 1./3.);
    return r;
  }//L1()
  public static double L2(double distance, double m1, double m2){
    double r = distance*Math.pow(m2/(3*m1), 1./3.);
    return r;
  }//L2()
  public static double L3(double distance, double m1, double m2){
    double r = 7./12.*distance*m2/m1;
    return r;
  }//L3()

  /**
  * This method calculates the required orbital velocity for a circular orbit
  * @param massBig double       this is the mass of the driving body
  * @param dis double           this is the starting distance between the two bodies
  * @return velocity double     this is velocity required for a circular orbit
  * @version 2018-05-16
  **/
  public static double circleVelocityG(double massBig, double dis){
    double velocity = Math.sqrt(G*massBig/dis);
    return velocity;
  }//circleVelocityG()

  /**
  * This method calculates the the angularVelocity of a body in circular gravitational motion
  * @param massBig double       this is the mass of the driving body
  * @param dis double           this is the distance between the two bodies
  * @return omega double        this is the angular velocity of the body
  * @version 2018-05-16
  **/
  public static double angularVelocity(double massBig, double dis){
    double omega = circleVelocityG(massBig, dis)/dis;
    return omega;
  }//angularVelocity()

  /**
  * This method calculates the orbital period of two bodies in circular gravitational motion
  * @param massBig double       this is the mass of the driving body
  * @param dis double           this is the distance between the two bodies
  * @return time double         this is the orbital period in hours
  * @version 2018-05-16
  **/
  public static double orbitalPeriod(double massBig, double dis){
    double time = 2*Math.PI/angularVelocity(massBig, dis);
    return time;
  }//orbitalPeriod()

  /**
  * This method converts the positions from cartesian to polar coordinates in order to make the plot relative to one body
  * @param body[][][][] double    these are the position, velocity, acceleration vectors for a body
  * @param inertiaNum int         this is the body number to use for the reference
  * @version 2018-05-18
  **/
  public static void inertialReference(double body[][][][], int inertiaNum){
    int bodies = body.length;
    int imax = body[0][0][0].length;
    double bodyTheta[][] = new double[bodies][imax];
    double inertiaTheta[] = new double[imax];
    double radial[][] = new double[bodies][imax];
    for (int bodynum=1;bodynum<bodyTheta.length;bodynum++) {
        for (int i=0;i<bodyTheta[0].length;i++) {
          if (body[bodynum][0][0][i]==0) {
            bodyTheta[bodynum][i]=Math.PI/2;
          }
          else {
            bodyTheta[bodynum][i]=Math.atan(body[bodynum][0][1][i]/body[bodynum][0][0][i]);
          }
          if (body[bodynum][0][0][i]<0) {
            bodyTheta[bodynum][i]+=Math.PI;
          }
          radial[bodynum][i]=BodyMaths.norm(body[bodynum][0][1][i],body[bodynum][0][0][i]);
        }
      }
      for (int i = 0;i<inertiaTheta.length;i++) {
        inertiaTheta[i]=bodyTheta[inertiaNum][i];
        for (int bodynum=0;bodynum<body.length;bodynum++) {
          bodyTheta[bodynum][i]-=inertiaTheta[i];
          body[bodynum][0][0][i]=radial[bodynum][i]*Math.cos(bodyTheta[bodynum][i]);
          body[bodynum][0][1][i]=radial[bodynum][i]*Math.sin(bodyTheta[bodynum][i]);
        }
      }
      inertiaTheta=null;
  }//inertialReference()


}//class