Control and stabilization of a rotating planar body with flexible attachments

2004 ◽  
Author(s):  
A.L. Zuyev
Keyword(s):  
Planar Body

scholarly journals CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR -BODY CHOREOGRAPHIES

2013 ◽  
Vol 1 ◽  
Author(s):  
JAMES MONTALDI ◽  
KATRINA STECKLES
Keyword(s):  
Braid Group ◽  
Connected Components ◽  
Symmetry Groups ◽  
Exceptional Groups ◽  
Strong Force ◽  
Symmetry Properties ◽  
Foundational Work ◽  
Force Potential ◽  
Planar Body

AbstractSince the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the $n$-body problem: periodic motions where the $n$ bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part, we classify all possible symmetry groups of planar $n$-body collision-free choreographies. These symmetry groups fall into two infinite families and, if $n$ is odd, three exceptional groups. In the second part, we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset. In particular, we refine the symmetry classification by classifying the connected components of the set of loops with any given symmetry. This leads to the existence of many new choreographies in $n$-body systems governed by a strong force potential.

Underwater maneuvering of robotic sheets through buoyancy-mediated active flutter

2021 ◽  
Vol 6 (53) ◽  
pp. eabe0637
Author(s):  
Junghwan Byun ◽  
Minjo Park ◽  
Sang-Min Baek ◽  
Jaeyoung Yoon ◽  
Woongbae Kim ◽  
...  
Keyword(s):  
Density Distribution ◽  
Environmental Remediation ◽  
Time Varying ◽  
Underwater Robots ◽  
Fluid Body ◽  
Planar Body

Falling leaves flutter from side to side due to passive and intrinsic fluid-body coupling. Exploiting the dynamics of passive fluttering could lead to fresh perspectives for the locomotion and manipulation of thin, planar objects in fluid environments. Here, we show that the time-varying density distribution within a thin, planar body effectively elicits minimal momentum control to reorient the principal flutter axis and propel itself via directional fluttery motions. We validated the principle by developing a swimming leaf with a soft skin that can modulate local buoyancy distributions for active flutter dynamics. To show generality and field applicability, we demonstrated underwater maneuvering and manipulation of adhesive and oil-skimming sheets for environmental remediation. These findings could inspire future intelligent underwater robots and manipulation schemes.

Conditions equivalent to central symmetry of convex curves

1964 ◽  
Vol 60 (4) ◽  
pp. 779-785 ◽  
Author(s):  
P. C. Hammer ◽  
T. Jefferson Smith
Keyword(s):  
Central Symmetry ◽  
Maximal Length ◽  
Convex Curves ◽  
The Family ◽  
Centrally Symmetric ◽  
Planar Body

In this paper we establish that a convex planar body C is centrally symmetric provided either one of the following conditions hold:(1) Each line halving the circumference of the boundary γ of C is a diametral line.(A diametral line is a line intersecting C in a chord of maximal length in the family of parallel chords.)(2) Each line halving the area of C is a diametral line.

scholarly journals Swim-like motion of bodies immersed in an ideal fluid

2019 ◽  
Vol 25 ◽  
pp. 16 ◽  
Author(s):  
Marta Zoppello ◽  
Franco Cardin
Keyword(s):  
Recent Literature ◽  
The Body ◽  
Riemann Mapping Theorem ◽  
First Order ◽  
Order Expansion ◽  
And Control ◽  
Small Deformations ◽  
Initial Impulse ◽  
Shape Changes ◽  
Planar Body

The connection between swimming and control theory is attracting increasing attention in the recent literature. Starting from an idea of Alberto Bressan [A. Bressan, Discrete Contin. Dyn. Syst. 20 (2008) 1–35]. we study the system of a planar body whose position and shape are described by a finite number of parameters, and is immersed in a 2-dimensional ideal and incompressible fluid in terms of gauge field on the space of shapes. We focus on a class of deformations measure preserving which are diffeomeorphisms whose existence is ensured by the Riemann Mapping Theorem. After making the first order expansion for small deformations, we face a crucial problem: the presence of possible non vanishing initial impulse. If the body starts with zero initial impulse we recover the results present in literature (Marsden, Munnier and oths). If instead the body starts with an initial impulse different from zero, the swimmer can self-propel in almost any direction if it can undergo shape changes without any bound on their velocity. This interesting observation, together with the analysis of the controllability of this system, seems innovative.

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