Comptes Rendus
no. 9
The tallest column problem: New first integrals and estimates
Teodor M. Atanackovic1
1 Faculty of Technical Sciences, University of Novi Sad, Serbia
Comptes Rendus. Mécanique, Volume 347 (2019) no. 9, pp. 626-631.

We analyze the problem of finding the shape of the tallest column. For the system of equations that determine the optimal shape we construct a variational principle and two new first integrals. From the first integrals we are able to determine, analytically, the size of the cross-sectional area of the optimal column at the bottom, as well as the corresponding bending moment and curvature of the elastic line. Our result for critical load is compared with the results obtained by other methods.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2019.09.001
Mots clés : Tallest column, Pontryagin's principle, First integrals
Teodor M. Atanackovic 1

1 Faculty of Technical Sciences, University of Novi Sad, Serbia 
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     doi = {10.1016/j.crme.2019.09.001},
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Teodor M. Atanackovic. The tallest column problem: New first integrals and estimates. Comptes Rendus. Mécanique, Volume 347 (2019) no. 9, pp. 626-631. doi : 10.1016/j.crme.2019.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.09.001/

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[3] S.J. Cox; C.M. McCarthy The shape of the tallest column: corrected, SIAM J. Math. Anal., Volume 31 (2000) (940–940)

[4] Y.V. Egorov On the optimization of higher eigenvalues, C. R. Mecanique, Volume 332 (2004), pp. 673-678

[5] Y.V. Egorov On the tallest column, C. R. Mecanique, Volume 338 (2010), pp. 266-270

[6] Y.V. Egorov On Euler's problem, Sb. Math., Volume 204 (2013), pp. 539-562

[7] J. Farjoun; J. Neu The tallest column—a dynamical system approach using a symmetry solution, Stud. Appl. Math., Volume 115 (2005), pp. 319-337

[8] J.B. Keller; F.I. Niordson The tallest column, J. Math. Mech., Volume 16 (1966), pp. 433-446

[9] B.D. Vujanovic; T.M. Atanackovic An Introduction to Modern Variational Techniques in Mechanics and Engineering, Birkhäuser, Boston, MA, USA, 2004

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