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📁 龙格库塔算法在VB下的实现
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VERSION 5.00
Begin VB.Form Form1 
   AutoRedraw      =   -1  'True
   BackColor       =   &H00000000&
   BorderStyle     =   1  'Fixed Single
   Caption         =   "卫星轨道"
   ClientHeight    =   6825
   ClientLeft      =   60
   ClientTop       =   345
   ClientWidth     =   8610
   DrawWidth       =   2
   FillColor       =   &H0000FFFF&
   BeginProperty Font 
      Name            =   "宋体"
      Size            =   12
      Charset         =   134
      Weight          =   400
      Underline       =   0   'False
      Italic          =   0   'False
      Strikethrough   =   0   'False
   EndProperty
   ForeColor       =   &H0000FFFF&
   LinkTopic       =   "Form1"
   LockControls    =   -1  'True
   MaxButton       =   0   'False
   MinButton       =   0   'False
   Moveable        =   0   'False
   ScaleHeight     =   6825
   ScaleWidth      =   8610
   WindowState     =   2  'Maximized
   Begin VB.CommandButton Command2 
      Caption         =   "退出"
      BeginProperty Font 
         Name            =   "宋体"
         Size            =   18
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      Height          =   855
      Left            =   11880
      TabIndex        =   8
      Top             =   9480
      Width           =   2535
   End
   Begin VB.CommandButton Command1 
      Caption         =   "清除"
      BeginProperty Font 
         Name            =   "宋体"
         Size            =   18
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      Height          =   855
      Left            =   11880
      TabIndex        =   7
      Top             =   8160
      Width           =   2535
   End
   Begin VB.TextBox Text2 
      Alignment       =   2  'Center
      BeginProperty Font 
         Name            =   "宋体"
         Size            =   24
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      Height          =   615
      Left            =   720
      TabIndex        =   6
      Text            =   "1"
      Top             =   1200
      Width           =   975
   End
   Begin VB.TextBox Text1 
      Alignment       =   2  'Center
      BeginProperty Font 
         Name            =   "仿宋_GB2312"
         Size            =   24
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      Height          =   615
      Left            =   720
      TabIndex        =   2
      Text            =   "8"
      Top             =   360
      Width           =   975
   End
   Begin VB.Label Label1 
      BackColor       =   &H00000000&
      Caption         =   "圈"
      BeginProperty Font 
         Name            =   "楷体_GB2312"
         Size            =   24
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      ForeColor       =   &H000000FF&
      Height          =   615
      Index           =   3
      Left            =   1800
      TabIndex        =   5
      Top             =   1200
      Width           =   495
   End
   Begin VB.Label Label1 
      BackColor       =   &H00000000&
      Caption         =   "转"
      BeginProperty Font 
         Name            =   "楷体_GB2312"
         Size            =   24
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      ForeColor       =   &H000000FF&
      Height          =   615
      Index           =   1
      Left            =   120
      TabIndex        =   4
      Top             =   1200
      Width           =   495
   End
   Begin VB.Label Label2 
      BackColor       =   &H00000000&
      Caption         =   "点击地球就发射"
      BeginProperty Font 
         Name            =   "楷体_GB2312"
         Size            =   26.25
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      ForeColor       =   &H0000C000&
      Height          =   495
      Left            =   240
      TabIndex        =   3
      Top             =   10200
      Width           =   5295
   End
   Begin VB.Label Label1 
      BackColor       =   &H00000000&
      Caption         =   "km/s"
      BeginProperty Font 
         Name            =   "楷体_GB2312"
         Size            =   24
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      ForeColor       =   &H000000FF&
      Height          =   615
      Index           =   2
      Left            =   1800
      TabIndex        =   1
      Top             =   360
      Width           =   975
   End
   Begin VB.Label Label1 
      BackColor       =   &H00000000&
      Caption         =   "v="
      BeginProperty Font 
         Name            =   "楷体_GB2312"
         Size            =   24
         Charset         =   134
         Weight          =   400
         Underline       =   0   'False
         Italic          =   0   'False
         Strikethrough   =   0   'False
      EndProperty
      ForeColor       =   &H000000FF&
      Height          =   615
      Index           =   0
      Left            =   120
      TabIndex        =   0
      Top             =   360
      Width           =   495
   End
   Begin VB.Image Image2 
      Appearance      =   0  'Flat
      Height          =   500
      Left            =   4995
      Picture         =   "卫星轨道.frx":0000
      Stretch         =   -1  'True
      Top             =   2160
      Visible         =   0   'False
      Width           =   500
   End
   Begin VB.Image Image1 
      Height          =   1380
      Left            =   7000
      Picture         =   "卫星轨道.frx":049F
      Top             =   5070
      Width           =   1380
   End
End
Attribute VB_Name = "Form1"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Dim i, n As Integer
Dim y(1, 1), dy(1, 1), ddy(1, 1), ddy_p(1), h, K, R, a, v, zoom As Double

Private Sub Command1_Click()
Cls
End Sub

Private Sub Command2_Click()
End
End Sub

Private Sub Form_Load()
n = 1                   '圈数

i = 1                   '开关

h = 1                 '步长

R = 6400                '地球半径

K = 401408              '重力系数

a = -K / R ^ 2          '系数

zoom = 0.3             '缩放系数

v = 10                   '速度初值

y(0, 0) = R             '矢径初值

y(1, 0) = 0             '角初值

dy(0, 0) = v            '矢径导数初值

dy(1, 0) = v / R        '角导数初值

End Sub

Private Sub Image1_Click()

'点击地球就发射

t$ = Text1.Text
nn$ = Text2.Text
v = Val(t$)
n = Val(nn$)

dy(0, 0) = v
dy(1, 0) = v / R

'判断是否是数字
If v = 0 Or n = 0 Then
MsgBox ("请输入正数字")
Text1.Text = ""
Text2.Text = ""
End If

'If v <= 7.9 Then Label2.Caption = "这样可上不了天!"
'If v >= 15.8 Then Label2.Caption = "这下该一去不复返了!"

'If v > 7.9 And v < 15.8 Then

 Image2.Visible = True
 
 Label2.Caption = "点击地球就发射"

 '二阶-龙格库塔法求轨道
 While (y(1, 0) <= n * 3.14159 * 2)

  Call equal

  '计算矢径
  dy(0, 1) = dy(0, 0) + ddy(0, 0) * h
  ddy(0, 1) = a + (y(0, 0) + dy(0, 1) * h) * dy(1, 0) ^ 2
  ddy_p(0) = (ddy(0, 0) + ddy(0, 1)) / 2
  dy(0, 1) = dy(0, 0) + ddy_p(0) * h
  y(0, 1) = y(0, 0) + (dy(0, 0) + dy(0, 1)) * h / 2

  '计算角度
  dy(1, 1) = dy(1, 0) + ddy(1, 0) * h
  ddy(1, 1) = -2 * dy(0, 1) * dy(1, 1) / y(0, 1)
  ddy_p(1) = (ddy(1, 0) + ddy(1, 1)) / 2
  dy(1, 1) = dy(1, 0) + ddy_p(1) * h
  y(1, 1) = y(1, 0) + (dy(1, 0) + dy(1, 1)) * h / 2

  Call gonext

  Call output

 Wend

'End If
 
Call orign

Image2.Visible = False

End Sub

Private Sub gonext()
'后一组前置
y(0, 0) = y(0, 1)
y(1, 0) = y(1, 1)
dy(0, 0) = dy(0, 1)
dy(1, 0) = dy(1, 1)
ddy(0, 0) = ddy(0, 1)
ddy(1, 0) = ddy(1, 1)
End Sub

Private Sub equal()
'原方程
ddy(0, 0) = a + y(0, 0) * dy(1, 0) ^ 2
ddy(1, 0) = -2 * dy(0, 0) * dy(1, 0) / y(0, 0)
End Sub

Private Sub output()
'卫星飞
Image2.Left = y(0, 1) * Cos(y(1, 1)) * zoom + 7380
Image2.Top = y(0, 1) * Sin(y(1, 1)) * zoom + 5460

'画轨道
i = -i
If i = 1 Then PSet (Image2.Left + 300, Image2.Top + 300)
End Sub

Private Sub orign()
y(0, 0) = R             '矢径初值

y(1, 0) = 0             '角初值

dy(0, 0) = v            '矢径导数初值

dy(1, 0) = v / R        '角导数初值
End Sub

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