Asymptotic lines on pseudospheres and the angle of parallelism

2021 ◽  
pp. 25-34
Author(s):  
Andrey Viktorovich Kostin ◽  
Keyword(s):  
Asymptotic Lines

scholarly journals Form-Finding of Shells Containing Both Tension and Compression Using the Airy Stress Function

2020 ◽  
Author(s):  
Masaaki Miki ◽  
Emil Adiels ◽  
William Baker ◽  
Toby Mitchell ◽  
Alexander Sehlstrom ◽  
...  
Keyword(s):  
Stress Function ◽  
Mixed Type ◽  
Airy Stress Function ◽  
Form Finding ◽  
Graphic Statics ◽  
Tension And Compression ◽  
Stress Functions ◽  
Complete Set ◽  
Pure Compression ◽  
Asymptotic Lines

Pure-compression shells have been the central topic in the form-finding of shells. This paper studies tension-compression mixed type shells by utilizing a NURBS-based isogeometric form-finding approach that analyzes Airy stress functions to expand the possible plan geometry. A complete set of smooth version graphic statics tools is provided to support the analyses. The method is validated using examples with known solutions, and a further example demonstrates the possible forms of shells that the proposed method permits. Additionally, a guideline to configure a proper set of boundary conditions is presented through the lens of asymptotic lines of the stress functions.

Complete structure of the Fučík spectrum of the p-Laplacian with integrable potentials on an interval

2016 ◽  
Vol 18 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Wei Chen ◽  
Jifeng Chu ◽  
Ping Yan ◽  
Meirong Zhang
Keyword(s):  
Double Sequence ◽  
Neumann Boundary ◽  
Strong Continuity ◽  
Complete Structure ◽  
Spectral Curves ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Differentiability Of Solutions ◽  
Asymptotic Lines ◽  
Fucik Spectrum

To characterize the complete structure of the Fučík spectrum of the [Formula: see text]-Laplacian on higher dimensional domains is a long-standing problem. In this paper, we study the [Formula: see text]-Laplacian with integrable potentials on an interval under the Dirichlet or the Neumann boundary conditions. Based on the strong continuity and continuous differentiability of solutions in potentials, we will give a comprehensive characterization of the corresponding Fučík spectra: each of them is composed of two trivial lines and a double-sequence of differentiable, strictly decreasing, hyperbolic-like curves; all asymptotic lines of these spectral curves are precisely described by using eigenvalues of the [Formula: see text]-Laplacian with potentials; and moreover, all these spectral curves have strong continuity in potentials, i.e. as potentials vary in the weak topology, these spectral curves are continuously dependent on potentials in a certain sense.

scholarly journals Parameterisation of developable surfaces by asymptotic lines

1996 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Vitaly Ushakov
Keyword(s):  
Explicit Form ◽  
Gaussian Curvature ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Asymptotic Lines

An example of a “non-developable” surface of vanishing Gaussian curvature from W. Klingenberg's textbook is considered and its place in the theory of 2-dimensional developable surfaces is pointed out. The surface is found in explicit form. Other examples of smooth developable surfaces not allowing smooth asymptotic parametrisation are analysed. In particular, Hartman and Nirenberg's example (1959) is incorrect.

Geometric invariants and principal configurations on spacelike surfaces immersed in ℝ3,1

2010 ◽  
Vol 140 (6) ◽  
pp. 1141-1160 ◽  
Author(s):  
Pierre Bayard ◽  
Federico Sánchez-Bringas
Keyword(s):  
Second Fundamental Form ◽  
Spacelike Surface ◽  
Geometric Invariants ◽  
Dimensional Minkowski Space ◽  
Numerical Invariants ◽  
Curvature Ellipse ◽  
Curvature Lines ◽  
The Mean ◽  
Asymptotic Lines ◽  
Spacelike Surfaces

We describe the numerical invariants and the curvature ellipse attached to the second fundamental form of a spacelike surface in a four-dimensional Minkowski space. We then study the configuration of the V-principal curvature lines on a spacelike surface when the normal field V is lightlike (the lightcone configuration). We end with some observations on the mean directionally curved lines and on the asymptotic lines on spacelike surfaces.

Extending the Theory of Dash Running

1982 ◽  
Vol 104 (3) ◽  
pp. 209-213 ◽  
Author(s):  
M. Senator
Keyword(s):  
Equation Of Motion ◽  
Time Axis ◽  
Tractive Force ◽  
World Record ◽  
Positive Power ◽  
Maximum Value ◽  
Force Velocity ◽  
Asymptotic Lines ◽  
Indoor And Outdoor

I extend the theory of dash running by allowing resisting force to be proportional to any positive power of speed and by allowing the runner to be tractive-force-limited at the beginning of the dash and developable-force-limited subsequently. I solve the equation of motion and express the maximum value of developable force as a function of limiting dash velocity, resisting-force/velocity exponent, and indoor and outdoor-track asymptotic intercept times (the intercepts with the time axis of asymptotic lines that are fitted to the distance-time curves) and limiting tractive coefficients. For a 20-yr-mean world record limiting dash velocity of 10.33 m/s and indoor and outdoor asymptotic intercept times of 0.617 and 0.265 s, I find that a composite dash world record holder is tractive-force-limited on indoor tracks, that limiting indoor tractive coefficient is about 0.9, and that the maximum value of developable force exceeds 2.0 times the record holder’s weight.

scholarly journals A note on the ruled surface

1937 ◽  
Vol 30 ◽  
pp. i-ii
Author(s):  
R. Wilson
Keyword(s):  
Mean Curvature ◽  
Geodesic Curvature ◽  
Ruled Surface ◽  
Local Geometry ◽  
Parametric Curves ◽  
The Mean ◽  
Curvature And Torsion ◽  
Asymptotic Lines ◽  
Special Case ◽  
Elegant Form

The generators and their orthogonal trajectories form, perhaps, the most useful set of parametric curves for the study of the local geometry of a ruled surface. It is not generally realised, however, that the fundamental quantities of the surface can be expressed quite simply in terms of the geodesic curvature, the geodesic torsion and the normal curvature of the directrix, that particular orthogonal trajectory which is chosen as base curve. Certain of the results are similar in form to those arising in the special case of a surface which is generated by the principal normals to a given curve, except that the curvature and torsion are geodetic. In addition it is possible to obtain in an elegant form the differential equation of the curved asymptotic lines and the expression for the mean curvature.

Sign in / Sign up

Export Citation Format

Share Document