forked from ShrohanMohapatra/ChaosInBH
-
Notifications
You must be signed in to change notification settings - Fork 0
/
ChaosEmptyAdSpoincare_DS_vs_NDS.nb
3337 lines (3278 loc) · 161 KB
/
ChaosEmptyAdSpoincare_DS_vs_NDS.nb
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
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 11.2' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 164238, 3329]
NotebookOptionsPosition[ 162612, 3271]
NotebookOutlinePosition[ 162959, 3286]
CellTagsIndexPosition[ 162916, 3283]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{"Needs", "[", "\"\<VariationalMethods`\>\"", "]"}]], "Input",
CellChangeTimes->{{3.767847376091784*^9, 3.7678473818475447`*^9}},
ExpressionUUID -> "063cc571-2c4f-4bce-b42a-d4e3b0d35198"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"EulerEquations", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"a", "/",
RowBox[{"y", "[", "t", "]"}]}], ")"}],
RowBox[{"Sqrt", "[",
RowBox[{"1", "-",
RowBox[{
RowBox[{
RowBox[{"y", "'"}], "[", "t", "]"}], "^", "2"}]}], "]"}]}], "+", " ",
RowBox[{"q", "/",
RowBox[{"y", "[", "t", "]"}]}]}], ",",
RowBox[{"y", "[", "t", "]"}], ",", "t"}], "]"}]], "Input",
ExpressionUUID -> "31590688-31f3-4e2a-a232-089beb94a9c5"],
Cell[BoxData[
RowBox[{
RowBox[{"-",
FractionBox[
RowBox[{"a", "+",
RowBox[{"q", " ",
SqrtBox[
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}]]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"], " ",
RowBox[{"(",
RowBox[{"a", "+",
RowBox[{"q", " ",
SqrtBox[
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}]]}]}], ")"}]}],
"-",
RowBox[{"a", " ",
RowBox[{"y", "[", "t", "]"}], " ",
RowBox[{
SuperscriptBox["y", "\[Prime]\[Prime]",
MultilineFunction->None], "[", "t", "]"}]}]}],
RowBox[{
SuperscriptBox[
RowBox[{"y", "[", "t", "]"}], "2"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}], ")"}],
RowBox[{"3", "/", "2"}]]}]]}], "\[Equal]", "0"}]], "Output",
ExpressionUUID -> "4ebff3ef-9084-49d4-adf5-295c456385f5"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"DSolve", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"-",
FractionBox[
RowBox[{"a", "+",
RowBox[{"q", " ",
SqrtBox[
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}]]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"], " ",
RowBox[{"(",
RowBox[{"a", "+",
RowBox[{"q", " ",
SqrtBox[
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}]]}]}],
")"}]}], "-",
RowBox[{"a", " ",
RowBox[{"y", "[", "t", "]"}], " ",
RowBox[{
SuperscriptBox["y", "\[Prime]\[Prime]",
MultilineFunction->None], "[", "t", "]"}]}]}],
RowBox[{
SuperscriptBox[
RowBox[{"y", "[", "t", "]"}], "2"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}], ")"}],
RowBox[{"3", "/", "2"}]]}]]}], "\[Equal]", "0"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"a", "\[Rule]", "1"}], ",",
RowBox[{"q", "\[Rule]",
RowBox[{"3", "/", "2"}]}]}], "}"}]}], ",",
RowBox[{
RowBox[{"y", "[", "0", "]"}], "\[Equal]", "1"}], ",",
RowBox[{
RowBox[{
RowBox[{"y", "'"}], "[", "0", "]"}], "\[Equal]", "0"}]}], "}"}], ",",
RowBox[{"y", "[", "t", "]"}], ",", "t"}], "]"}]], "Input"],
Cell[BoxData[
TemplateBox[{
"Solve","ifun",
"\"Inverse functions are being used by \
\\!\\(\\*RowBox[{\\\"Solve\\\"}]\\), so some solutions may not be found; use \
Reduce for complete solution information.\"",2,52,91,31607805995628520914,
"Local"},
"MessageTemplate"]], "Message", "MSG"],
Cell[BoxData[
TemplateBox[{
"Solve","ifun",
"\"Inverse functions are being used by \
\\!\\(\\*RowBox[{\\\"Solve\\\"}]\\), so some solutions may not be found; use \
Reduce for complete solution information.\"",2,52,92,31607805995628520914,
"Local"},
"MessageTemplate"]], "Message", "MSG"],
Cell[BoxData[
TemplateBox[{
"Solve","ifun",
"\"Inverse functions are being used by \
\\!\\(\\*RowBox[{\\\"Solve\\\"}]\\), so some solutions may not be found; use \
Reduce for complete solution information.\"",2,52,93,31607805995628520914,
"Local"},
"MessageTemplate"]], "Message", "MSG"],
Cell[BoxData[
TemplateBox[{
"General","stop",
"\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"Solve\\\", \\\"::\\\", \
\\\"ifun\\\"}], \\\"MessageName\\\"]\\) will be suppressed during this \
calculation.\"",2,52,94,31607805995628520914,"Local"},
"MessageTemplate"]], "Message", "MSG"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"y", "[", "t", "]"}], "\[Rule]",
RowBox[{"3", "-",
SqrtBox[
RowBox[{"4", "+",
SuperscriptBox["t", "2"]}]]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"y", "[", "t", "]"}], "\[Rule]",
RowBox[{
FractionBox["1", "5"], " ",
RowBox[{"(",
RowBox[{"3", "+",
SqrtBox[
RowBox[{"4", "+",
RowBox[{"25", " ",
SuperscriptBox["t", "2"]}]}]]}], ")"}]}]}], "}"}]}],
"}"}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"3", "-",
SqrtBox[
RowBox[{"4", "+",
SuperscriptBox["t", "2"]}]]}], ",",
RowBox[{
FractionBox["1", "5"], " ",
RowBox[{"(",
RowBox[{"3", "+",
SqrtBox[
RowBox[{"4", "+",
RowBox[{"25", " ",
SuperscriptBox["t", "2"]}]}]]}], ")"}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV03k4lfkXAPBrqeyDyvrG1auUZMxv1MTE+U7yy0ieZpDGKIObW5EpW5Im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"]]},
Annotation[#, "Charting`Private`Tag$794717#1"]& ],
TagBox[
{RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV0Hk01AsbB3BMZC+UrDPDbyaSukhJr+l5Sqo7SguqSyWTTG6FyBLaNCUt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"]]},
Annotation[#, "Charting`Private`Tag$794717#2"]& ]}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
Part[#, 1]],
(Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
Part[#, 1]],
(Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 10}, {-7.198038827067064, 10.607996598638879`}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"3", "-",
SqrtBox[
RowBox[{"4", "+",
SuperscriptBox["t", "2"]}]]}], "/.",
RowBox[{"t", "\[Rule]", "3"}]}], ",",
RowBox[{
RowBox[{"2", "-",
SqrtBox[
RowBox[{"1", "+",
SuperscriptBox["t", "2"]}]]}], "/.",
RowBox[{"t", "\[Rule]", "3"}]}], ",",
RowBox[{
RowBox[{
FractionBox["1", "2"], " ",
RowBox[{"(",
RowBox[{"1", "+",
SqrtBox[
RowBox[{"1", "+",
RowBox[{"4", " ",
SuperscriptBox["t", "2"]}]}]]}], ")"}]}], "/.",
RowBox[{"t", "\[Rule]", "3"}]}], ",",
RowBox[{
RowBox[{
RowBox[{"-", "1"}], "+",
SqrtBox[
RowBox[{"4", "+",
SuperscriptBox["t", "2"]}]]}], "/.",
RowBox[{"t", "\[Rule]", "3"}]}], ",",
RowBox[{
RowBox[{
FractionBox["1", "3"], " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "1"}], "+",
SqrtBox[
RowBox[{"16", "+",
RowBox[{"9", " ",
SuperscriptBox["t", "2"]}]}]]}], ")"}]}], "/.",
RowBox[{"t", "\[Rule]", "3"}]}]}], "}"}], "//", "N"}]], "Input"],
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"-", "0.6055512754639891`"}], ",",
RowBox[{"-", "1.1622776601683795`"}], ",", "3.5413812651491097`", ",",
"2.605551275463989`", ",", "2.949619267265368`"}], "}"}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"3", "-",
SqrtBox[
RowBox[{"4", "+",
SuperscriptBox["t", "2"]}]]}], ",",
RowBox[{"2", "-",
SqrtBox[
RowBox[{"1", "+",
SuperscriptBox["t", "2"]}]]}], ",",
RowBox[{
FractionBox["1", "2"], " ",
RowBox[{"(",
RowBox[{"1", "+",
SqrtBox[
RowBox[{"1", "+",
RowBox[{"4", " ",
SuperscriptBox["t", "2"]}]}]]}], ")"}]}], ",",
RowBox[{
RowBox[{"-", "1"}], "+",
SqrtBox[
RowBox[{"4", "+",
SuperscriptBox["t", "2"]}]]}], ",",
RowBox[{
FractionBox["1", "3"], " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "1"}], "+",
SqrtBox[
RowBox[{"16", "+",
RowBox[{"9", " ",
SuperscriptBox["t", "2"]}]}]]}], ")"}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "5"}], "}"}]}], "]"}]], "Input"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwd03s4lHkbB/AxI3JImN6WkoaVU3R417aI7mfDKnmlxSZbxMYoVrIpSSUR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"]]},
Annotation[#, "Charting`Private`Tag$377030#1"]& ],
TagBox[
{RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV0ns41PkXB3AM+br+8P09korJKpfkl7baUpxPrJKs1U+qn7UsYYSE6IIi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"]]},
Annotation[#, "Charting`Private`Tag$377030#2"]& ],
TagBox[
{RGBColor[0.560181, 0.691569, 0.194885], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV0nk4lIsXB/BhhuzLvGZKhNYpSZRuCOdEWnC1SEmLa8KkUjc3ciVJi2SX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"]]},
Annotation[#, "Charting`Private`Tag$377030#3"]& ],
TagBox[
{RGBColor[0.922526, 0.385626, 0.209179], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwd03k41dkfB/DLRVzX8vWdkcpy65clu6Y0ij4nMkoyCjEyGpLLKEWUkSRZ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"]]},
Annotation[#, "Charting`Private`Tag$377030#4"]& ],
TagBox[
{RGBColor[0.528488, 0.470624, 0.701351], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwV1Hk01ekfB/DLRXb33u/U0NgTEqUpU1Q+HxmZbpJCGW1jvUSSX6ZCSRHK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"]]},
Annotation[#, "Charting`Private`Tag$377030#5"]& ]}, {}, {}},
AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
Axes->{True, True},
AxesLabel->{None, None},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
Frame->{{False, False}, {False, False}},
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLines->{None, None},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
Part[#, 1]],
(Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
Part[#, 1]],
(Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 5}, {-3.099019413533532, 5.524937709026037}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output"]
}, Open ]],
Cell[BoxData[""], "Input"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Block", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{",
RowBox[{"y1", ",", "y2", ",", "dy", ",", "py"}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"y1", "[",
RowBox[{"a1_", ",", "ys_", ",", "q1_"}], "]"}], ":=",
RowBox[{"NDSolveValue", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"-",
FractionBox[
RowBox[{"a", "+",
RowBox[{"q", " ",
SqrtBox[
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}]]}], "-",
RowBox[{
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"], " ",
RowBox[{"(",
RowBox[{"a", "+",
RowBox[{"q", " ",
SqrtBox[
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}]]}]}],
")"}]}], "-",
RowBox[{"a", " ",
RowBox[{"y", "[", "t", "]"}], " ",
RowBox[{
SuperscriptBox["y", "\[Prime]\[Prime]",
MultilineFunction->None], "[", "t", "]"}]}]}],
RowBox[{
SuperscriptBox[
RowBox[{"y", "[", "t", "]"}], "2"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"1", "-",
SuperscriptBox[
RowBox[{
SuperscriptBox["y", "\[Prime]",
MultilineFunction->None], "[", "t", "]"}], "2"]}], ")"}],
RowBox[{"3", "/", "2"}]]}]]}], "\[Equal]", "0"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"a", "\[Rule]", "a1"}], ",",
RowBox[{"q", "\[Rule]", "q1"}]}], "}"}]}], ",",
RowBox[{
RowBox[{"y", "[", "0", "]"}], "\[Equal]", "ys"}], ",",
RowBox[{
RowBox[{
RowBox[{"y", "'"}], "[", "0", "]"}], "\[Equal]", "0"}]}], "}"}],
",",
RowBox[{"y", "[", "t", "]"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "20"}], "}"}]}], "]"}]}], ";",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"y2", "[",
RowBox[{"t1_", ",", "a_", ",", "ys_", ",", "q_"}], "]"}], ":=",
RowBox[{
RowBox[{"y1", "[",
RowBox[{"a", ",", "ys", ",", "q"}], "]"}], "/.",
RowBox[{"{",
RowBox[{"t", "\[Rule]", "t1"}], "}"}]}]}], ";", "\[IndentingNewLine]",
RowBox[{"Print", "[", "\[IndentingNewLine]",
RowBox[{"Show", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"ListLinePlot", "[",
RowBox[{
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{"i", ",",
RowBox[{"y2", "[",
RowBox[{"i", ",", "1", ",", "1", ",", "0.01"}], "]"}]}], "}"}],
",",
RowBox[{"{",
RowBox[{"i", ",", "0", ",", "20", ",", "0.05"}], "}"}]}], "]"}],
",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"t", ",", "y"}], "}"}]}]}], "]"}], ",",
"\[IndentingNewLine]",
RowBox[{"ListLinePlot", "[",
RowBox[{
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{"i", ",",
RowBox[{"y2", "[",
RowBox[{"i", ",", "1", ",", "1", ",", "300"}], "]"}]}], "}"}],
",",
RowBox[{"{",
RowBox[{"i", ",", "0", ",", "20", ",", "0.05"}], "}"}]}], "]"}],
",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"t", ",", "y"}], "}"}]}], ",",
RowBox[{"PlotStyle", "\[Rule]", "Green"}]}], "]"}]}],
"\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", "]"}], ";"}]}],
"\[IndentingNewLine]", "]"}]], "Input"],
Cell[BoxData[
GraphicsBox[{{{}, {{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[
0.011111111111111112`], AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJxV1mdUU1m4xvEgIFV6IBBaEhIglDQFRoXzXsECoyKKYi+oYIcZbIMi2MVx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