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Considering the case of air damping, we use the method of numerical simulation to study dynamic behavior of inelastic bouncing ball. By changing the value of control parameter V0, the motion of the bouncing ball exhibits nonlinear phenomena of period doubling bifurcation, chaos, etc. These phenomena are confirmed by both 0-1 test and maximal Lyapunov exponent.
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Keywords:
- inelastic bouncing ball /
- 0-1 test /
- chaos /
- granular material
[1] Fermi E 1949 Phys. Rev. 75 1169
[2] Lichtenberg A J, Liebermen M A, Cohen R H 1980 Physica D 1 291
[3] Jaeger H M, Nagel S R, Bringer R P 1996 Rev. Mod. Phys. 68 1259
[4] Evesque P, Rajchenbach J 1989 Phys. Rev. Lett. 62 44
[5] Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[6] Aoki K M, Akiyama T, Maki Y, Watanabe T 1996 Phys. Rev. E 54 874
[7] Melo F, Umbanhowar P, Swinney H L 1994 Phys. Rev. Lett. 72 172
[8] Visscher W M, Bolsterli M 1972 Nature 239 504
[9] Hong D C, Quinn P V, Luding S 2011 Phys. Rev. Lett. 86 3423
[10] Quinn P V, Hong D C 2000 Phys. Rev. E 62 8295
[11] Zhao Y Z, Jiang M Q, Zheng J Y 2009 Acta Phys Sin. 58 1812 (in Chinese) [赵永志, 江茂强, 郑津洋 2009 58 1812]
[12] Jiang Z H, Lu K Q, Hou M Y, Chen W, Chen X J 2003 Acta Phys. Sin. 52 2244 (in Chinese) [姜泽辉, 陆坤权, 厚美瑛, 陈唯, 陈相君 2003 52 2244]
[13] Shi Q F, Yan X Q, Hou M Y, Niu X J, Lu K Q 2003 Chin. Sci. Bull. 48 328 (in Chinese) [史庆藩, 阎学群, 厚美瑛, 牛小娟, 陆坤权 2003 科学通报 48 328]
[14] Liang X W, Li L S, Hou Z G, Lü Z, Yang L, Sun G, Shi Q F 2008 Acta Phys. Sin. 57 2300 (in Chinese) [梁宣文, 李粮生, 侯兆国, 吕震, 杨雷, 孙刚, 史庆藩 2008 57 2300]
[15] Sun Q C, Wang G Q 2009 Granular Material Mechanics Introduction (Beijing: Science Press) pp7-10 (in Chinese) [孙其诚, 王光谦 2009 颗粒物质力学导论(北京:科学出版社) 第7-10页]
[16] Giusepponi S, Marchesoni F, Borromeo M 2005 Physica A 351 142
[17] Warr S, Cooke W, Ball R C, Huntley J M 1996 Physica A 231 551
[18] Linz S J, Hänggi P 1994 Phys. Rev. E 50 3464
[19] Kowalik Z J, Franaszek M, Pierarński P 1988 Phys. Rev. A 37 4016
[20] Pierarński P, Malécki J 1986 Phys. Rev. A 34 582
[21] Paskota M 1998 Chaos Soliton Fract. 9 323
[22] Franaszek M, Isomäki H M 1991 Phys. Rev. A 43 4231
[23] Tufillaro N B 1994 Phys. Rev. E 50 4590
[24] Holmes P J 1982 J. Sound Vibration 84 173
[25] Naylor M A 2002 Phys. Rev. E 66 057201
[26] Everson R M 1986 Physica D 19 355
[27] Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese) [姜泽辉, 赵海发, 郑瑞华 2009 58 7579]
[28] Jiang Z H, Zheng R H, Zhao H F, Wu J 2007 Acta Phys. Sin. 56 3727 [姜泽辉, 郑瑞华, 赵海发, 吴晶 2007 56 3727]
[29] Gilet T, Vandewalle N, Dorbolo S 2009 Phys. Rev. E 79 055201
[30] Bennetin G, Galgani L, Giorgilli A, Strelcyn J M 1978 C. R. Acad. Sc. Paris A 268 431
[31] Gottwald G A, Melbourne I 2004 Proc. R. Soc. Lond. A 406 603
[32] Litak G, Syta A, Budhraja M, Saha L M 2009 Chaos Soliton. Fract. 42 1511
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[1] Fermi E 1949 Phys. Rev. 75 1169
[2] Lichtenberg A J, Liebermen M A, Cohen R H 1980 Physica D 1 291
[3] Jaeger H M, Nagel S R, Bringer R P 1996 Rev. Mod. Phys. 68 1259
[4] Evesque P, Rajchenbach J 1989 Phys. Rev. Lett. 62 44
[5] Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[6] Aoki K M, Akiyama T, Maki Y, Watanabe T 1996 Phys. Rev. E 54 874
[7] Melo F, Umbanhowar P, Swinney H L 1994 Phys. Rev. Lett. 72 172
[8] Visscher W M, Bolsterli M 1972 Nature 239 504
[9] Hong D C, Quinn P V, Luding S 2011 Phys. Rev. Lett. 86 3423
[10] Quinn P V, Hong D C 2000 Phys. Rev. E 62 8295
[11] Zhao Y Z, Jiang M Q, Zheng J Y 2009 Acta Phys Sin. 58 1812 (in Chinese) [赵永志, 江茂强, 郑津洋 2009 58 1812]
[12] Jiang Z H, Lu K Q, Hou M Y, Chen W, Chen X J 2003 Acta Phys. Sin. 52 2244 (in Chinese) [姜泽辉, 陆坤权, 厚美瑛, 陈唯, 陈相君 2003 52 2244]
[13] Shi Q F, Yan X Q, Hou M Y, Niu X J, Lu K Q 2003 Chin. Sci. Bull. 48 328 (in Chinese) [史庆藩, 阎学群, 厚美瑛, 牛小娟, 陆坤权 2003 科学通报 48 328]
[14] Liang X W, Li L S, Hou Z G, Lü Z, Yang L, Sun G, Shi Q F 2008 Acta Phys. Sin. 57 2300 (in Chinese) [梁宣文, 李粮生, 侯兆国, 吕震, 杨雷, 孙刚, 史庆藩 2008 57 2300]
[15] Sun Q C, Wang G Q 2009 Granular Material Mechanics Introduction (Beijing: Science Press) pp7-10 (in Chinese) [孙其诚, 王光谦 2009 颗粒物质力学导论(北京:科学出版社) 第7-10页]
[16] Giusepponi S, Marchesoni F, Borromeo M 2005 Physica A 351 142
[17] Warr S, Cooke W, Ball R C, Huntley J M 1996 Physica A 231 551
[18] Linz S J, Hänggi P 1994 Phys. Rev. E 50 3464
[19] Kowalik Z J, Franaszek M, Pierarński P 1988 Phys. Rev. A 37 4016
[20] Pierarński P, Malécki J 1986 Phys. Rev. A 34 582
[21] Paskota M 1998 Chaos Soliton Fract. 9 323
[22] Franaszek M, Isomäki H M 1991 Phys. Rev. A 43 4231
[23] Tufillaro N B 1994 Phys. Rev. E 50 4590
[24] Holmes P J 1982 J. Sound Vibration 84 173
[25] Naylor M A 2002 Phys. Rev. E 66 057201
[26] Everson R M 1986 Physica D 19 355
[27] Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese) [姜泽辉, 赵海发, 郑瑞华 2009 58 7579]
[28] Jiang Z H, Zheng R H, Zhao H F, Wu J 2007 Acta Phys. Sin. 56 3727 [姜泽辉, 郑瑞华, 赵海发, 吴晶 2007 56 3727]
[29] Gilet T, Vandewalle N, Dorbolo S 2009 Phys. Rev. E 79 055201
[30] Bennetin G, Galgani L, Giorgilli A, Strelcyn J M 1978 C. R. Acad. Sc. Paris A 268 431
[31] Gottwald G A, Melbourne I 2004 Proc. R. Soc. Lond. A 406 603
[32] Litak G, Syta A, Budhraja M, Saha L M 2009 Chaos Soliton. Fract. 42 1511
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