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Animal Shapes, Modal Analysis, and Visualization of Motion (II): Dynamics and Fourier Decomposition

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Abstract

This paper begins with solving the linear elastodynamic equation with forcing by expanding it into Fourier series. We then proceed to prove the conservation laws of momentum, angular momentum, and energy. We intend the paper to provide a computational demonstration for modal analysis by showing that eigenmodes and frequencies of vibration of a free-suspending horse match with the modal analysis results of the horse after a short-impulse impact of the horse with a wall. The horse CAD model has to be modified to contain a rigid body portion to prevent the rotational-tumbling modes. A fast Fourier transform is applied to the sensorial time series data in the calculation of the vibration frequencies. One can see that many low-frequency modes and data match these modal analysis results.

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Acknowledgements

We thank Prof. Jan Sokolowski for helpful suggestions. Tiexin Guo is supported by the National Natural Science Foundation of China (No.11671278 and No.11971483) and the Science and Technology Research Project of Chongqing Municipal Education Commission(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. Chunqiu Wei is supported by the Research Ability Improvement Program for Young Teachers of BUCEA (Grant No. X21031).

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Authors and Affiliations

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

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

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

    Goong Chen

  3. Hsinchu Branch, National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu, Taiwan, ROC

    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, ROC

    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, 410075, Hunan, China

    Tiexin Guo

Authors
  1. Goong Chen
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  2. Chunqiu Wei
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  3. Alexey Sergeev
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  4. Jing Yang
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  5. Jingtong Kaya Huang
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  6. Matthew M. Scully
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  7. Ming-Chieh Chen
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  8. Steven G. Krantz
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  9. Pengfei Yao
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  10. Tiexin Guo
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  11. Junmin Wang
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Correspondence to Goong Chen.

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G. Chen—on Development Leave from Texas A &M University.

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Chen, G., Wei, C., Sergeev, A. et al. Animal Shapes, Modal Analysis, and Visualization of Motion (II): Dynamics and Fourier Decomposition. J Geom Anal 33, 309 (2023). https://doi.org/10.1007/s12220-023-01342-6

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