Table 2

Some characteristic values for the forward speed v and the eigenvalues λ from the linearized stability analysis for the benchmark bicycle from figure 1 and table 1. (Fourteen-digit results are presented for benchmark comparisons. (a) v=0, weave speed vw, capsize speed vc and the speed with a double root vd. In the forward speed range of 0≤v≤10 m s−1, (b) complex (weave motion) eigenvalues λweave and (c) real eigenvalues λ.)

(a)

v (m s−1)λ (s−1)
v=0λs1=±3.131 643 247 906 56
v=0λs2=±5.530 943 717 653 93
vd=0.684 283 078 892 46λd=3.782 904 051 293 20
vw=4.292 382 536 341 11λw=0±3.435 033 848 661 44 i
vc=6.024 262 015 388 370

(b)
v (m s−1)Re(λweave) (s−1)Im(λweave) (s−1)
0
13.526 961 709 900 700.807 740 275 199 30
22.682 345 175 127 451.680 662 965 906 75
31.706 756 056 639 752.315 824 473 843 25
40.413 253 315 211 253.079 108 186 032 06
5−0.775 341 882 195 854.464 867 713 788 23
6−1.526 444 865 841 425.876 730 605 987 09
7−2.138 756 442 583 627.195 259 133 298 05
8−2.693 486 835 810 978.460 379 713 969 31
9−3.216 754 022 524 859.693 773 515 317 91
10−3.720 168 404 372 8710.906 811 394 762 87

(c)
v (m s−1)λcapsize (s−1)λcastering (s−1)
0−3.131 643 247 906 56−5.530 943 717 653 93
1−3.134 231 250 665 78−7.110 080 146 374 42
2−3.071 586 456 415 14−8.673 879 848 317 35
3−2.633 661 372 536 67−10.351 014 672 459 20
4−1.429 444 273 613 26−12.158 614 265 764 47
5−0.322 866 429 004 09−14.078 389 692 798 22
6−0.004 066 900 769 70−16.085 371 230 980 26
70.102 681 705 747 66−18.157 884 661 252 62
80.143 278 797 657 13−20.279 408 943 945 69
90.157 901 840 309 17−22.437 885 590 408 58
100.161 053 386 531 72−24.624 596 350 174 04