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Chaplygin problem

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191: 42:. Specifically, the problem is to determine what flight path an airplane in a constant wind field should take in order to encircle the maximum possible area in a given amount of time. The airplane is assumed to be constrained to move in a plane, moving at a constant 232: 256: 106: 251: 225: 218: 175: 39: 28: 198: 157: 24: 116: 102: 98: 149: 128: 202: 245: 91: 86: 190: 20: 36: 43: 161: 61: 140:
Klamkin, M. S.; Newman, D. J. (1969). "Flying in a wind field I, II".
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The solution of the problem is that the airplane should travel in an
53:, and the wind is assumed to move in a constant direction with speed 153: 132: 148:(1). Mathematical Association of America: 16–23, pp. 1013–1019. 206: 90: 226: 8: 233: 219: 119:(1976). "On Extreme length flight paths". 64:whose major axis is perpendicular to 7: 187: 185: 35:is an isoperimetric problem with a 14: 189: 23:, particularly in the fields of 97:. New York: Blasidel. pp.  16:Solved question in mathematics 1: 205:. You can help Knowledge by 178: : zero wind speed case 273: 184: 93:The Calculus of variations 257:Applied mathematics stubs 176:Isoperimetric inequality 252:Calculus of variations 201:-related article is a 29:calculus of variations 68:, with eccentricity 199:applied mathematics 142:Amer. Math. Monthly 25:nonlinear dynamics 214: 213: 33:Chaplygin problem 264: 235: 228: 221: 193: 186: 165: 136: 112: 96: 272: 271: 267: 266: 265: 263: 262: 261: 242: 241: 240: 239: 182: 172: 154:10.2307/2316780 139: 133:10.1137/1018079 115: 109: 87:Akhiezer, N. I. 85: 82: 17: 12: 11: 5: 270: 268: 260: 259: 254: 244: 243: 238: 237: 230: 223: 215: 212: 211: 194: 180: 179: 171: 168: 167: 166: 137: 127:(2): 486–488. 117:Klamkin, M. S. 113: 107: 81: 78: 15: 13: 10: 9: 6: 4: 3: 2: 269: 258: 255: 253: 250: 249: 247: 236: 231: 229: 224: 222: 217: 216: 210: 208: 204: 200: 195: 192: 188: 183: 177: 174: 173: 169: 163: 159: 155: 151: 147: 143: 138: 134: 130: 126: 122: 118: 114: 110: 108:3-7186-4805-9 104: 100: 95: 94: 88: 84: 83: 79: 77: 75: 71: 67: 63: 58: 56: 52: 48: 45: 41: 38: 34: 30: 26: 22: 207:expanding it 196: 181: 145: 141: 124: 120: 92: 73: 69: 65: 59: 54: 50: 46: 37:differential 32: 18: 121:SIAM Review 49:, for time 21:mathematics 246:Categories 80:References 40:constraint 170:See also 89:(1962). 44:airspeed 27:and the 162:2316780 99:206–208 62:ellipse 160:  105:  31:, the 197:This 158:JSTOR 203:stub 103:ISBN 150:doi 129:doi 19:In 248:: 156:. 146:76 144:. 125:18 123:. 101:. 76:. 57:. 234:e 227:t 220:v 209:. 164:. 152:: 135:. 131:: 111:. 74:v 72:/ 70:w 66:w 55:w 51:T 47:v

Index

mathematics
nonlinear dynamics
calculus of variations
differential
constraint
airspeed
ellipse
Akhiezer, N. I.
The Calculus of variations
206–208
ISBN
3-7186-4805-9
Klamkin, M. S.
doi
10.1137/1018079
doi
10.2307/2316780
JSTOR
2316780
Isoperimetric inequality
Stub icon
applied mathematics
stub
expanding it
v
t
e
Categories
Calculus of variations
Applied mathematics stubs

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