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Animal Shapes, Modal Analysis, and Visualization of Motion (III): Giraffe, Duck, Goose, T-Rex Dinosaur, and the Flying Modes of Eagle

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Abstract

This paper contains more varieties of animals, including the giraffe, bird species duck, goose and eagle, and the T-Rex dinosaur. They range across mammals, birds and reptiles. For each of them, we present their first one hundred modes of motion. Three objectives of this paper are as follows:

  1. (i)

    To see more different types of modes of motion from a larger varieties of animals so as to make visual comparisons between interspecies behavioral patterns.

  2. (ii)

    To illustrate the wing-flapping flying modes of an eagle.

  3. (iii)

    To show the modes of motions of an extinct animal, the T-Rex dinosaur.

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References

  1. Chen, G., Huang, J., Wei, C., Yang, J., Scully, M.M., Sergeev, A., Chen, M.-C., Krantz, S.G., Yao, P., Guo, T., Wang, J.: Animal shapes, modal analysis, and visualization of motion (I): horse and camel. J. Geom. Anal. https://doi.org/10.1007/s12220-023-01339-1

  2. Petzl Techniques & Products, Giraffe 3D Model. https://c4ddownload.com/giraffe-3d-model/

  3. Amazing giraffe facts you need to know!. https://www.youtube.com/watch?v=ERjyMHa1igs/

  4. Download 3d models (of a duck). https://downloadfree3d.com/interior/animals/duck/

  5. Swan 17 (a goose 3d cad model). https://3dwarehouse.sketchup.com/model/u223c6bbf-d484-4d4c-9d57-a74c4fcca1eb/Swan-17

  6. Eagle 3d model. https://done3d.com/eagle/

  7. Plotnikov, P.I., Sokolowski, J.: Optimal shape control of airfoil in compressible gas flow governed by Navier–Stokes equations. Evol. Equ. Control Theory 2, 495–516 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Plotnikov, P., Sokołowski, J.: Compressible Navier–Stokes Equations: Theory and Shape Optimization, vol. 73. Springer, New York (2012)

    Book  MATH  Google Scholar 

  9. Blender Market, Dinosaur Base Mesh-Mega Pack (3D models for dinosaurs). https://blendermarket.com/products/dinosaur-base-mesh-mega-pack

  10. Chen, G., Wei, C., Sergeev, A., Yang, J., Huang, J.K., Scully, M.M., Chen, M.-C., Krantz, S.G., Yao, P., Guo, T., Wang, J.: Animal shapes, modal analysis, and visualization of motion (II): dynamics and Fourier decomposition

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Acknowledgements

We thank Randi D. Ruden for suggesting the study of modal analysis of a flying eagle and other birds. We also thank Prof. Jan Sokolowski for helpful suggestions and constructive comments. Tiexin Guo is supported by the National Natural Science Foundation of China (Grant Nos. 11671278 and 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 Nos. 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. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 102488, China

    Jing Yang & Junmin Wang

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

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

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

    Goong Chen

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

    Goong Chen

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

    Chunqiu Wei

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

    Steven G. Krantz

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

    Pengfei Yao

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

    Pengfei Yao

  9. School of Mathematics and Statistice, Central South University, Changsha, 410075, Hunan, China

    Tiexin Guo

  10. Department of Mechanical Engineering, Cheng Shiu University, Kaohsiung, Taiwan, ROC

    Ming-Chieh Chen

  11. Corti Brothers, 5810 Folsom Blvd., Sacramento, CA, 95819, USA

    Darrell Corti

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  1. Jing Yang
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  2. Goong Chen
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  3. Chunqiu Wei
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  5. Jingtong Huang
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  7. Steven G. Krantz
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  8. Pengfei Yao
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  9. Tiexin Guo
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  10. Junmin Wang
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  11. Ming-Chieh Chen
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  12. Darrell Corti
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Correspondence to Goong Chen.

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Goong Chen: on Development Leave from Texas A &M University.

Appendix: CAD Parameters for Modal Computations

Appendix: CAD Parameters for Modal Computations

See Table 2.

Table 2 Parameter values of the animal: giraffe, duck, goose, eagle, crane, and T-Rex dinosaur, used in modal computations. (These values should not be regarded as canonical values.)
Full size table

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Yang, J., Chen, G., Wei, C. et al. Animal Shapes, Modal Analysis, and Visualization of Motion (III): Giraffe, Duck, Goose, T-Rex Dinosaur, and the Flying Modes of Eagle. J Geom Anal 33, 325 (2023). https://doi.org/10.1007/s12220-023-01344-4

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  • DOI: https://doi.org/10.1007/s12220-023-01344-4

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