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Animal Shapes, Modal Analysis, and Visualization of Motion (I): Horse and Camel

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Abstract

Eigenfunctions and eigenvalues of physical systems and engineering structures can reveal many of the system’s fundamental features and, therefore, become a basis for the study of inverse problems. In this series of papers, we take a reverse, direct-problem point of view; namely, given the shapes of animals, can we see the patterns of their motions or behaviors through their eigenmode analysis? This modal analysis, we believe, has never been done for living animals. Our modal analysis emphasizes dynamics, which is achieved by visualization through video animation by incorporating the time-harmonic dependence of the eigenmodes. Furthermore, we intend our modal analysis to be more realistic by encompassing the situation of the presence of a floor. Certain physical interpretations of the motion patterns from modal analysis are made. In addition, by visualization, one can see that symmetry plays an important role in motion patterns. One of our main conclusions is that shapes alone can usefully reflect or explain some animal’s behavior or motion patterns.

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Acknowledgements

We thank Prof. Jan Sokolowski for invaluable suggestions and constructive comments. Chunqiu Wei is supported by the Research Ability Improvement Program for Young Teachers of BUCEA (Grant No. X21031). Tiexin Guo is supported by the National Natural Science Foundation of China (Grant No. 11971483) and the Science and Technology Research Project of Chongqing Municipal Education Commission (Grant No. KJ1706154). Pengfei Yao is supported in part by the National Science Foundation of China, grant No. 12071463, and by the special fund for Science and Technology Innovation Teams of Shanxi Province, Grants # 202204051002015. Junmin Wang is supported in part by the National Natural Science Foundation of China No. 62073037 and 12131008.

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Authors and Affiliations

  1. Department of Mathematics, Texas A &M University, College Station, TX, 77843, USA

    Goong Chen, Jingtong Huang, Matthew M. Scully & Alexey Sergeev

  2. Institute for Quantum Science and Engineering, Texas A &M University, College Station, TX, 77843, USA

    Goong Chen

  3. National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu Branch, Hsinchu, Taiwan, R.O.C.

    Goong Chen

  4. Department of Mathematics and Data Science, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Chunqiu Wei

  5. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Jing Yang & Junmin Wang

  6. Department of Mechanical Engineering, Cheng Shiu University, Kaohsiung, 83347, Taiwan, R.O.C.

    Ming-Chieh Chen

  7. Department of Mathematics, Washington University at St. Louis, St. Louis, MO, 63130, USA

    Steven G. Krantz

  8. Key Laboratory of Complex Systems and Data Science of Ministry of Education, School of Mathematics Shanxi University, Taiyuan, 030006, Shanxi, China

    Pengfei Yao

  9. Institute of Systems Science Academy of Mathematics and Systems Science, Academia Sinica, Beijing, 100190, China

    Pengfei Yao

  10. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China

    Tiexin Guo

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  1. Goong Chen
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Appendix: Frequencies of vibrations of the horse and camel

Appendix: Frequencies of vibrations of the horse and camel

Table 2 The frequencies of modal analysis of, respectively, the horse and camel without floor or with floor. Note that the first 6 frequencies are actually zero (i.e., trivial). The rest 100 frequencies are nonzero. Therefore, we have included a total of 106 frequencies in the table
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Chen, G., Huang, J., Wei, C. et al. Animal Shapes, Modal Analysis, and Visualization of Motion (I): Horse and Camel. J Geom Anal 33, 328 (2023). https://doi.org/10.1007/s12220-023-01339-1

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