BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 88(1) 70-80 2013年8月 [査読有り]
The Kirchhoff elastic rod is one of the mathematical models of equilibrium configurations of thin elastic rods, and is defined to be a solution of the Euler-Lagrange equations associated to the energy with the effect of bending and twisting. In th...
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 87(1) 5-9 2011年1月 [査読有り]
In this paper, we give examples of Kirchhoff rod centerlines fully immersed in higher-dimensional space forms. More precisely, we prove that any helix in a space form is a Kirchhoff rod centerline. These examples imply the difference of the geomet...
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 60(2) 551-582 2008年4月 [査読有り]
The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is characterized as a critical point of the energy functional obtained by adding the effect of twisting to the bending energy. In this paper, we investigate Kirc...
The Kirchhoff elastic rod is one of the mathematical models of thin elastic rods, and is a critical point of the energy functional with the effect of bending and twisting. In this paper, we study Kirchhoff elastic rods in the three-sphere of const...
Imagine a thin elastic rod like a piano wire. We consider the situation that the elastic rod is bent and twisted and both ends are welded together to form a smooth loop. Then, does there exist a stable equilibrium? In this paper, we generalize the...