-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathContinuous_Beam_Buckling.nb
8345 lines (8147 loc) · 411 KB
/
Continuous_Beam_Buckling.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 12.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 412716, 8337]
NotebookOptionsPosition[ 397926, 8067]
NotebookOutlinePosition[ 398322, 8083]
CellTagsIndexPosition[ 398279, 8080]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["Trave continua", "Title",
CellChangeTimes->{{3.8430231482344465`*^9,
3.843023150245099*^9}},ExpressionUUID->"717bbce6-7c50-4c4c-8a1a-\
209f68bbca37"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"v1", "[", "s1_", "]"}], " ", "=", " ",
RowBox[{"c1", "+",
RowBox[{"c2", "*", "s1"}], "+",
RowBox[{"c3", "*",
RowBox[{"Cos", "[",
RowBox[{"\[Alpha]", "*", "s1"}], "]"}]}], "+",
RowBox[{"c4", "*",
RowBox[{"Sin", "[",
RowBox[{"\[Alpha]", "*", "s1"}], "]"}]}]}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"v2", "[", "s2_", "]"}], " ", "=", " ",
RowBox[{"c5", "+",
RowBox[{"c6", "*", "s2"}], "+",
RowBox[{"c7", "*",
RowBox[{"Cos", "[",
RowBox[{"\[Alpha]", "*", "s2"}], "]"}]}], "+",
RowBox[{"c8", "*",
RowBox[{"Sin", "[",
RowBox[{"\[Alpha]", "*", "s2"}], "]"}]}]}]}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{"RR", ",", " ", "MM"}], "}"}], " ", "=", " ",
RowBox[{
RowBox[{"CoefficientArrays", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"v1", "[", "0", "]"}], "==", "0"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"v1", "''"}], "[", "0", "]"}], "==", "0"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"v1", "[", "l", "]"}], "==", "0"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{"v2", "[", "0", "]"}], "==", "0"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"v1", "'"}], "[", "l", "]"}], "==",
RowBox[{
RowBox[{"v2", "'"}], "[", "0", "]"}]}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"v1", "''"}], "[", "l", "]"}], "==",
RowBox[{
RowBox[{"v2", "''"}], "[", "0", "]"}]}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{"v2", "[", "l", "]"}], "==", "0"}], ",",
"\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"v2", "''"}], "[", "l", "]"}], "==", "0"}]}],
"\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
"c1", ",", " ", "c2", ",", " ", "c3", ",", " ", "c4", ",", " ", "c5",
",", " ", "c6", ",", " ", "c7", ",", " ", "c8"}], "}"}]}],
"\[IndentingNewLine]", "]"}], "//", "Normal"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"RR", " ", "=", " ",
RowBox[{"-", "RR"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"MatrixForm", "[", "MM", "]"}], "\[IndentingNewLine]",
RowBox[{"MatrixForm", "[", "RR", "]"}]}], "Input",
CellChangeTimes->{{3.842957199934647*^9, 3.842957408681201*^9}},
CellLabel->"In[83]:=",ExpressionUUID->"9884f33e-c2b9-4f10-9850-2479bef9205f"],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{"1", "0", "1", "0", "0", "0", "0", "0"},
{"0", "0",
RowBox[{"-",
SuperscriptBox["\[Alpha]", "2"]}], "0", "0", "0", "0", "0"},
{"1", "l",
RowBox[{"Cos", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}],
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}], "0", "0", "0", "0"},
{"0", "0", "0", "0", "1", "0", "1", "0"},
{"0", "1",
RowBox[{
RowBox[{"-", "\[Alpha]"}], " ",
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}],
RowBox[{"\[Alpha]", " ",
RowBox[{"Cos", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}], "0",
RowBox[{"-", "1"}], "0",
RowBox[{"-", "\[Alpha]"}]},
{"0", "0",
RowBox[{
RowBox[{"-",
SuperscriptBox["\[Alpha]", "2"]}], " ",
RowBox[{"Cos", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}],
RowBox[{
RowBox[{"-",
SuperscriptBox["\[Alpha]", "2"]}], " ",
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}], "0", "0",
SuperscriptBox["\[Alpha]", "2"], "0"},
{"0", "0", "0", "0", "1", "l",
RowBox[{"Cos", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}],
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]},
{"0", "0", "0", "0", "0", "0",
RowBox[{
RowBox[{"-",
SuperscriptBox["\[Alpha]", "2"]}], " ",
RowBox[{"Cos", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}],
RowBox[{
RowBox[{"-",
SuperscriptBox["\[Alpha]", "2"]}], " ",
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{3.842957409226494*^9},
CellLabel->
"Out[88]//MatrixForm=",ExpressionUUID->"34d09c73-ddf7-485d-98d6-\
74ec64a4e53c"],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]",
TagBox[GridBox[{
{"0"},
{"0"},
{"0"},
{"0"},
{"0"},
{"0"},
{"0"},
{"0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.5599999999999999]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}],
Column], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{3.842957409235462*^9},
CellLabel->
"Out[89]//MatrixForm=",ExpressionUUID->"477e65a0-c513-4c2f-aadb-\
8c1c23af52dc"]
}, Closed]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"detMM", "[", "\[Alpha]_", "]"}], "=",
RowBox[{
RowBox[{"Det", "[", "MM", "]"}], "//", "Simplify"}]}]], "Input",
CellChangeTimes->{{3.842957412355088*^9, 3.842957428257601*^9}},
CellLabel->"In[90]:=",ExpressionUUID->"2773423f-91ef-4a90-b7f4-9de852705d34"],
Cell[BoxData[
RowBox[{
RowBox[{"-", "2"}], " ", "l", " ",
SuperscriptBox["\[Alpha]", "6"], " ",
RowBox[{"(",
RowBox[{
RowBox[{"l", " ", "\[Alpha]", " ",
RowBox[{"Cos", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}], "-",
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}], ")"}], " ",
RowBox[{"Sin", "[",
RowBox[{"l", " ", "\[Alpha]"}], "]"}]}]], "Output",
CellChangeTimes->{3.8429574302475567`*^9},
CellLabel->"Out[90]=",ExpressionUUID->"043b964a-f430-4c6f-ba0c-21a180fa16a4"]
}, Open ]],
Cell[CellGroupData[{
Cell["Primo modo critico", "Subtitle",
CellChangeTimes->{{3.842965122720686*^9,
3.842965125464875*^9}},ExpressionUUID->"509c3581-5df9-45cb-b92b-\
ac99216dff18"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"detMM", "[", "\[Alpha]", "]"}], ",", " ",
RowBox[{"{",
RowBox[{"\[Alpha]", ",", " ", "0", ",", " ", "5"}], "}"}], ",", " ",
RowBox[{"PlotRange", "\[Rule]", "Full"}]}], "]"}]], "Input",
CellChangeTimes->{{3.8429622300606413`*^9, 3.842962248475178*^9}, {
3.8429650589440775`*^9, 3.842965060356058*^9}},
CellLabel->
"In[314]:=",ExpressionUUID->"f3fd8a11-974f-412c-8809-47fb8edb370b"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
1.], LineBox[CompressedData["
1:eJwVV3c8lu8XlvFaxWukSEgiO1FKvOdkJaESUiSJSIhSVJRkZCYpNKz4ZitR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"]]},
Annotation[#, "Charting`Private`Tag$84404#1"]& ]}, {}},
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,
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" ->
AbsolutePointSize[6], "ScalingFunctions" -> None,
"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& ), "CopiedValueFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
PlotRange->{{0, 5}, {-11960.122395458504`, 71237.12069646415}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.05],
Scaled[0.05]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.842962242634411*^9, 3.842962248876853*^9},
3.8429650608735495`*^9, 3.8430197068890243`*^9},
CellLabel->
"Out[314]=",ExpressionUUID->"d66c89f0-80a4-491e-83b3-a233340ebeb4"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"\[Alpha]", "/.",
RowBox[{"FindRoot", "[",
RowBox[{
RowBox[{
RowBox[{"detMM", "[", "\[Alpha]", "]"}], "==", "0"}], ",", " ",
RowBox[{"{",
RowBox[{"\[Alpha]", ",", " ", "3"}], "}"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.8429650649977612`*^9, 3.8429650881005993`*^9}},
CellLabel->
"In[315]:=",ExpressionUUID->"8d00f253-8c33-402c-a87e-5634a095f58e"],
Cell[BoxData["3.1415926535897936`"], "Output",
CellChangeTimes->{{3.8429650817757797`*^9, 3.8429650883896723`*^9},
3.8430197081185308`*^9},
CellLabel->
"Out[315]=",ExpressionUUID->"ebaa62e4-c9a2-4cf4-b71a-8d1e8c959ef0"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{"ClearAll", "[",
RowBox[{"\[Alpha]cr", ",", " ", "l", ",", "k"}],
"]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"l", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"\[Alpha]cr", " ", "=", " ",
RowBox[{"Simplify", "[",
RowBox[{"k", "*",
FractionBox["Pi", "l"]}], "]"}]}], ";"}],
"\[IndentingNewLine]"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"MMcr", " ", "=", " ",
RowBox[{
RowBox[{"Simplify", "[",
RowBox[{
RowBox[{"MM", "/.",
RowBox[{"\[Alpha]", "->", "\[Alpha]cr"}]}], ",", " ",
RowBox[{"Assumptions", "\[Rule]",
RowBox[{"k", " ", "\[Element]", " ", "Integers"}]}]}], "]"}], "//",
"Chop"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"MatrixForm", "[", "MMcr", "]"}]}], "Input",
CellChangeTimes->{{3.842961464996541*^9, 3.8429615155998697`*^9}, {
3.842961559241434*^9, 3.842961598592246*^9}, {3.842961695190392*^9,
3.842961762173156*^9}, {3.8429618905974984`*^9, 3.8429618979683046`*^9}, {
3.843019718266474*^9, 3.843019718564836*^9}},
CellLabel->
"In[322]:=",ExpressionUUID->"e302cc69-2cf0-4fbf-83b4-8978641b6589"],
Cell[BoxData[
TagBox[
RowBox[{"(", "\[NoBreak]", GridBox[{
{"1", "0", "1", "0", "0", "0", "0", "0"},
{"0", "0",
RowBox[{
RowBox[{"-",
SuperscriptBox["k", "2"]}], " ",
SuperscriptBox["\[Pi]", "2"]}], "0", "0", "0", "0", "0"},
{"1", "1",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "k"], "0", "0", "0", "0", "0"},
{"0", "0", "0", "0", "1", "0", "1", "0"},
{"0", "1", "0",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "k"], " ", "k", " ", "\[Pi]"}], "0",
RowBox[{"-", "1"}], "0",
RowBox[{
RowBox[{"-", "k"}], " ", "\[Pi]"}]},
{"0", "0",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+", "k"}]], " ",
SuperscriptBox["k", "2"], " ",
SuperscriptBox["\[Pi]", "2"]}], "0", "0", "0",
RowBox[{
SuperscriptBox["k", "2"], " ",
SuperscriptBox["\[Pi]", "2"]}], "0"},
{"0", "0", "0", "0", "1", "1",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "k"], "0"},
{"0", "0", "0", "0", "0", "0",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"1", "+", "k"}]], " ",
SuperscriptBox["k", "2"], " ",
SuperscriptBox["\[Pi]", "2"]}], "0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], "\[NoBreak]", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]], "Output",
CellChangeTimes->{
3.8429615159364634`*^9, {3.842961570427608*^9, 3.842961598829924*^9},
3.842961697108431*^9, {3.8429617400355043`*^9, 3.842961762531459*^9}, {
3.842961894115054*^9, 3.8429618983333607`*^9}, 3.842965091477863*^9, {
3.843019710134427*^9, 3.8430197190308404`*^9}},
CellLabel->
"Out[326]//MatrixForm=",ExpressionUUID->"edb5679f-5d6d-4781-aff7-\
78f8e8e037ca"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{
RowBox[{"{",
RowBox[{
"c1", ",", " ", "c2", ",", " ", "c3", ",", " ", "c4", ",", " ", "c5", ",",
" ", "c6", ",", " ", "c7", ",", " ", "c8"}], "}"}], " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{"Eigenvectors", "[", "MMcr", "]"}], "[",
RowBox[{"[", "1", "]"}], "]"}], "//", "Chop"}]}]], "Input",
CellChangeTimes->{{3.8429615194886904`*^9, 3.8429615239369593`*^9}, {
3.8429617551811857`*^9, 3.8429617699919014`*^9}, {3.8429619337419786`*^9,
3.8429619534176135`*^9}, {3.8429620081996636`*^9, 3.842962012443133*^9}},
CellLabel->
"In[327]:=",ExpressionUUID->"ec629162-8a8d-4d0d-bcdc-d3dd67d5084d"],
Cell[BoxData[
RowBox[{"{",
RowBox[{"0", ",", "0", ",", "0", ",",
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "-", "k"}]], ",", "0", ",", "0", ",", "0", ",", "1"}],
"}"}]], "Output",
CellChangeTimes->{
3.842961539707902*^9, {3.8429617337870374`*^9, 3.8429617705731134`*^9},
3.8429618998505907`*^9, {3.842961934322523*^9, 3.8429619541650352`*^9}, {
3.842962008896095*^9, 3.842962012970643*^9}, {3.843019711503093*^9,
3.843019721049694*^9}},
CellLabel->
"Out[327]=",ExpressionUUID->"2f456009-5736-4483-a2d3-025308b99c7b"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{"v1", "[", "s1", "]"}], "\[IndentingNewLine]",
RowBox[{"v2", "[", "s2", "]"}]}], "Input",
CellChangeTimes->{{3.842961955990938*^9, 3.842961961113494*^9}, {
3.842962015851824*^9, 3.8429620336561427`*^9}},
CellLabel->
"In[328]:=",ExpressionUUID->"23901fce-b9bf-4455-8a5c-7c71248cd63e"],
Cell[BoxData[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"-", "1"}], ")"}],
RowBox[{"2", "-", "k"}]], " ",
RowBox[{"Sin", "[",
RowBox[{"s1", " ", "\[Alpha]"}], "]"}]}]], "Output",
CellChangeTimes->{
3.842961961447133*^9, {3.842962016932955*^9, 3.842962034288305*^9},
3.8430197219584756`*^9},
CellLabel->
"Out[328]=",ExpressionUUID->"ccd16876-5f20-4c11-8280-2eb3a034d148"],
Cell[BoxData[
RowBox[{"Sin", "[",
RowBox[{"s2", " ", "\[Alpha]"}], "]"}]], "Output",
CellChangeTimes->{
3.842961961447133*^9, {3.842962016932955*^9, 3.842962034288305*^9},
3.843019721966047*^9},
CellLabel->
"Out[329]=",ExpressionUUID->"d256cf7c-a21d-4cc3-936b-3fcbfa5be3f1"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"k", "=", "1"}], ";"}], "\[IndentingNewLine]",
RowBox[{"Show", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{"v1", "[", "s", "]"}], "/.",
RowBox[{"\[Alpha]", "->", "\[Alpha]cr"}]}], ",", " ",
RowBox[{"{",
RowBox[{"s", ",", " ", "0", ",", " ", "l"}], "}"}], ",", " ",
RowBox[{"ScalingFunctions", "\[Rule]", "\"\<Reverse\>\""}]}], "]"}], ",",
"\[IndentingNewLine]",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{
RowBox[{"v2", "[",
RowBox[{"s", "-", "l"}], "]"}], "/.",
RowBox[{"\[Alpha]", "->", "\[Alpha]cr"}]}], ",", " ",
RowBox[{"{",
RowBox[{"s", ",", " ", "l", ",", " ",
RowBox[{"2", "l"}]}], "}"}], ",", " ",
RowBox[{"ScalingFunctions", "\[Rule]", "\"\<Reverse\>\""}]}], "]"}], ",",
"\[IndentingNewLine]",
RowBox[{"PlotRange", "->", "Full"}]}], "\[IndentingNewLine]",
"]"}]}], "Input",
CellChangeTimes->{{3.842962023243052*^9, 3.842962181482543*^9}, {
3.842965015974224*^9, 3.8429650247666636`*^9}, {3.8429650972399435`*^9,
3.842965100568618*^9}},
CellLabel->
"In[330]:=",ExpressionUUID->"5c411306-16bb-4603-990f-3b2fa81c1b1c"],
Cell[BoxData[
GraphicsBox[{{{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwd2HlYTN8fB/AWRBKlvilZQkRRkZKlN4pQqRQJFVm+CWkjS2QplJRChTay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"]]},
Annotation[#, "Charting`Private`Tag$86300#1"]& ]}, {}}, {{{}, {},
TagBox[
{RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6],
Opacity[1.], LineBox[CompressedData["
1:eJwd2Hk8VO0XAHD0liVkLUqUUvYlslUOfqJIlkTJlja8FVLRm61QqWR9pbJk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