Moments and Forces on General Convex Bodies in Hypersonic Flow

AIAA Journal ◽  
1974 ◽  
Vol 12 (9) ◽  
pp. 1241-1247 ◽  
Author(s):  
JACK PIKE
Keyword(s):  
Hypersonic Flow ◽  
Convex Bodies ◽  
General Convex

Asymptotic Formulae for the Lattice Point Enumerator

1999 ◽  
Vol 51 (2) ◽  
pp. 225-249 ◽  
Author(s):  
U. Betke ◽  
K. Böröczky
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Positive Curvature ◽  
Convex Bodies ◽  
Mixed Volume ◽  
Lattice Points ◽  
Asymptotic Formulae ◽  
General Convex ◽  
Lattice Surface ◽  
Small Deformations

AbstractLet M be a convex body such that the boundary has positive curvature. Then by a well developed theory dating back to Landau and Hlawka for large λ the number of lattice points in λM is given by G(λM) = V(λM) + O(λd−1−ε(d)) for some positive ε(d). Here we give for general convex bodies the weaker estimatewhere SZd (M) denotes the lattice surface area of M. The term SZd is optimal for all convex bodies and o(λd−1) cannot be improved in general. We prove that the same estimate even holds if we allow small deformations of M.Further we deal with families {Pλ} of convex bodies where the only condition is that the inradius tends to infinity. Here we havewhere the convex body K satisfies some simple condition, V(Pλ; K; 1) is some mixed volume and S(Pλ) is the surface area of Pλ.

Stable Lattices

1953 ◽  
Vol 5 ◽  
pp. 261-270 ◽  
Author(s):  
Harvey Cohn
Keyword(s):  
Convex Body ◽  
Finite Number ◽  
Quadratic Forms ◽  
Convex Bodies ◽  
Lattice Points ◽  
Three Dimensions ◽  
General Convex ◽  
Critical Lattice ◽  
The Absolute

The consideration of relative extrema to correspond to the absolute extremum which is the critical lattice has been going on for some time. As far back as 1873, Korkine and Zolotareff [6] worked with the ellipsoid in hyperspace (i.e., with quadratic forms), and later Minkowski [8] worked with a general convex body in two or three dimensions. They showed how to find critical lattices by selection from among a finite number of relative extrema. They were aided by the long-recognized premise that only a finite number of lattice points can enter into consideration [1] when one deals with lattices “admissible to convex bodies.”

Christoffel's problem for general convex bodies

Mathematika ◽  
1968 ◽  
Vol 15 (1) ◽  
pp. 7-21 ◽  
Author(s):  
William J. Firey
Keyword(s):  
Convex Bodies ◽  
General Convex

Dynamics of an axisymmetric body spinning on a horizontal surface. III. Geometry of steady state structures for convex bodies

2005 ◽  
Vol 462 (2066) ◽  
pp. 371-390 ◽  
Author(s):  
M Branicki ◽  
H.K Moffatt ◽  
Y Shimomura
Keyword(s):  
Fixed Point ◽  
Convex Bodies ◽  
Axisymmetric Body ◽  
Steady States ◽  
The Body ◽  
Dimensional System ◽  
Centre Of Mass ◽  
Tippe Top ◽  
General Convex ◽  
Axisymmetric Bodies

Following parts I and II of this series, the geometry of steady states for a general convex axisymmetric rigid body spinning on a horizontal table is analysed. A general relationship between the pedal curve of the cross-section of the body and the height of its centre-of-mass above the table is obtained which allows for a straightforward determination of static equilibria. It is shown, in particular, that there exist convex axisymmetric bodies having arbitrarily many static equilibria. Four basic categories of non-isolated fixed-point branches (i.e. steady states) are identified in the general case. Depending on the geometry of the spinning body and its dynamical properties (i.e. position of centre-of-mass and inertia tensor), these elementary branches are differently interconnected in the six-dimensional system phase space and form a complex global structure. The geometry of such structures is analysed and topologically distinct classes of configurations are identified. Detailed analysis is presented for a spheroid with displaced centre-of-mass and for the tippe-top. In particular, it is shown that the fixed-point structure of the flip-symmetric spheroid, discussed in part I, represents a degenerate configuration whose degeneracy is destroyed by breaking the symmetry. For the spheroid, there are in general nine distinct classes of fixed-point structures and for the tippe-top there are three such structures. Bifurcations between these classes are identified in the parameter space of the system.

Numerical Simulation of the Effect of Porous Cooling of Bodies in Hypersonic Flow

2002 ◽  
Vol 33 (1-2) ◽  
pp. 8
Author(s):  
Alexander I. Leontiev ◽  
V. V. Nosatov ◽  
G. S. Sadovnikov
Keyword(s):  
Numerical Simulation ◽  
Hypersonic Flow
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