Euler Elastica Terminal Parafoil Guidance

Physical systems such as an inverted pendulum driven by a spiral spring, an unbalanced Euler elastica with a travelling mass, a heavy body with a parabolic section and an Ising ferromagnet are very different. However, they all behave in the same manner close to the critical regime for which nonlinearities are prominent. We demonstrate experimentally, for the first time, an old prediction by Joseph Larmor, which states that a nonlinear oscillator close to its supercritical bifurcation oscillates with a period inversely proportional to its angular amplitude. We perform our experiments with a Holweck–Lejay-like pendulum which was used to measure the gravity field during the twentieth century.

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Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2012031 ◽

2013 ◽

Vol 19 (3) ◽

pp. 740-753 ◽

Cited By ~ 1

Author(s):

Luca Mugnai

Keyword(s):

Phase Field ◽

Gamma Convergence ◽

Euler Elastica ◽

Convergence Results

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Euler Elastica Regularized Logistic Regression for Whole-Brain Decoding of fMRI Data

IEEE Transactions on Biomedical Engineering ◽

10.1109/tbme.2017.2756665 ◽

2018 ◽

Vol 65 (7) ◽

pp. 1639-1653 ◽

Cited By ~ 3

Author(s):

Chuncheng Zhang ◽

Li Yao ◽

Sutao Song ◽

Xiaotong Wen ◽

Xiaojie Zhao ◽

...

Keyword(s):

Logistic Regression ◽

Fmri Data ◽

Whole Brain ◽

Brain Decoding ◽

Euler Elastica

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Agile Finite Difference Approach to Euler Elastica Visualization

Scientific Visualization ◽

10.26583/sv.11.3.02 ◽

2019 ◽

Vol 11 (3) ◽

Author(s):

E.V. Popov ◽

T.P. Popova

Keyword(s):

Finite Difference ◽

Euler Elastica ◽

Finite Difference Approach

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Magneto-elastic buckling of an Euler beam

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2013.0111 ◽

2013 ◽

Vol 469 (2155) ◽

pp. 20130111 ◽

Cited By ~ 7

Author(s):

K. Singh ◽

C. R. Tipton ◽

E. Han ◽

T. Mullin

Keyword(s):

Magnetic Field ◽

Elastic Beam ◽

Separation Distance ◽

Magnetic Interactions ◽

Euler Beam ◽

Euler Elastica ◽

Close Proximity ◽

Observed Behaviour ◽

Nonlinear Elastic ◽

Bifurcation Behaviour

We consider nonlinear elastic deformations of a magneto-elastic beam, using a combined experimental and theoretical approach. In the experiments, a beam had one end clamped with a magnet attached at its free end. When it was placed in an external magnetic field, it was susceptible to Euler beam buckling. However, the classic supercritical bifurcation associated with this buckling became subcritical when an attracting magnet was introduced in close proximity to the beam. To understand these experiments, we develop a model that couples the Euler elastica and dipole magnetic interactions with a uniform external field. The numerical model captures the observed behaviour well and shows that the supercritical magnetic field strength depends almost exclusively on elastic properties of the beam and strength of the permanent magnet, whereas the subcritical behaviour also depends on the separation distance between the attracting pair of magnets. We examine the bifurcation behaviour of the nonlinear system and show that for sufficiently small inter-magnet separation distances, other buckled states coexist with the fundamental mode.

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