On Sudden Cessation in Circular Motion
This short paper presents a simple analytical model for the abrupt termination of circular motion, as discussed in the "The Most Mind-Blowing Aspect of Circular Motion".
physics.gen-ph↗
arXiv subjects
Milan Batista
Publications and source records attributed to Milan Batista.
Large deflections and stability of spring-hinged cantilever beam
In the article, we investigate the influence of spring on the large deflections and stability of a spring-hinged cantilever subject to conservative tip force. Using the closed form solution of the equilibrium equation and closed form solution of Jacobi accessory equation, we determine the beam equilibrium forms and their stability. Also, the solution for spring-hinged cantilever bema subject to a follower force is given. Results are present in the graphical and the tabular form.
physics.class-ph↗
On Stability of Non-inflectional Elastica
This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the Dirichlet boundary conditions is unconditionally stable, while for the other two boundary conditions, sufficient criteria for stability depend on the signs of the second derivatives of the tangent angle at the endpoints.
physics.class-ph↗
On the axisymmetric post-buckling of a thin elastic circular plate under uniform edge pressure
In this paper, we revised a post-buckling of an elastic circular plate subject to uniform pressure on its edge. The governing von Karman equations are solved by power series method and numerical colocation method. An alternative method for calculation of coefficients of the series solution is described. It is shown that the power series solution is useful only for the first buckling mode while collocation method can handle also higher buckling modes.
physics.class-ph↗
Elfun18 A collection of Matlab functions for the computation of Elliptical Integrals and Jacobian elliptic functions of real arguments
In the article we outline the set of Matlab functions that enable the computation of elliptic Integrals and Jacobian elliptic functions for real arguments. Correctness, robustness, efficiency and accuracy of the functions are discussed in some details. An example from the elasticity theory illustrates use of the collection.
cs.MS↗
A Note on a Generalization of Sherman-Morrison-Woodbury formula
The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).
math-ph↗
A Closed Form Solution for Reissner's Planar Finite-Strain Beam Using Jacobi Elliptical Functions
In the article we introduce an analytical solution for Reissner's large-deflection finite-strain planar beam subject to an end force and a bending moment. The solution is given in terms of Jacobi elliptical functions. The obtained analytical solution is enhanced with numerical examples. A buckling and post buckling behavior of a beam under axial compressive load applied at the end and subject to various boundary conditions is also discussed in some details. In particular, the buckling factor is derived for each case of the boundary conditions.
physics.class-ph↗
On composite conformal mapping of an annulus to a plane with two holes
In the article we consider the composite conformal map which maps annulus to infinite region with symmetric hole and nearly circular hole. It is shown that such transformation is good if the distance between centers of holes are large or radius of circular hole is small. Examples for bilinear-hypotrochoids mapping and bilinear-Schwarz-Christoffel mapping are present.
math.CV↗
Jacobi's epsilon and zeta function for moduli outside the interval [0, 1]
The formulas that relate Jacobi's Epsilon and Zeta function with real moduli in the interval (1,inf) or with pure imaginary moduli to elliptic functions with moduli in the interval [0,1] are derived.
math.CA↗
On Jacobi's condition for the simplest problem of calculus of variations with mixed boundary conditions
The purpose of this paper is the extension of Jacobi's criteria for positive definiteness of second variation of the simplest problems of calculus of variations subject to mixed boundary conditions. Both non constrained and isoperimetric problems are discussed. The main result is that Jacobi's condition remains valid also for the mixed boundary conditions.
math.GM↗
Large Deflections of Beam Subject to Three-points Bending
In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with results of other authors. Approximation formula by which the beam load is given as polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical example.
physics.class-ph↗
Large Deflection of Cantilever Rod Pulled by Cable
The article discusses six problems which can arise in the determination of the equilibrium configuration of an elastic cantilever rod pulled by an inextensible cable. The discussions are illustrated with graphs of equilibrium shapes and tables providing some reference numerical values.
physics.gen-ph↗
Equilibrium Configurations of Cantilever under Terminal Loads
The paper provides an exact analytical solution for equilibrium configurations of cantilever rod subject to inclined force and torque acting on its free end. The solution is given in terms of Jacobi elliptical functions and illustrated by several numerical examples and several graphical presentations of shapes of deformed cantilever. Possible forms of cantilever underlying elastica are discussed in details and various simple formulas are given for calculation of characteristic dimensions of elastica. For the case when cantilever is subject only to applied force four load conditions are discussed: follower load problem, load determination problem, conservative load problem and rotational load problem. For all the cases the formulas or effective procedure for solution is given.
physics.gen-ph↗
Some methods of estimating uncertainty in accident reconstruction
In the paper four methods for estimating uncertainty in accident reconstruction are discussed: total differential method, extreme values method, Gauss statistical method, and Monte Carlo simulation method. The methods are described and the program solutions are given.
physics.gen-ph↗
Analytical solution for free vibrations of simply supported transversally inextensible homogeneous rectangular plate
In article, the exact solution of sinusoidal loaded simply supported elastic transversally inextensible rectangular plate is given. The expressions for displacement and stress components are derived and asymptotic expansion with respect to plate thickness are present. The frequency factors for plate thickness to width ratio 0.01, 0.1, 0.2 and 0.4 and various ratios of plate length to width are given.
physics.gen-ph↗
Uniformly Loaded Rectangular Thin Plates with Symmetrical Boundary Conditions
In the article the Fourier series analytical solutions of uniformly loaded rectangular thin plates with symmetrical boundary conditions are considered. For all the cases the numerical values are tabulated.
physics.gen-ph↗
A Simple Throw Model for Frontal Vehicle-Pedestrian Collisions
This paper discusses a simple theoretical throw model for frontal vehicle-pedestrian collisions. The model is based on the simple assumption that pedestrian movement after impact can be approximated by movement of a mass point. Two methods of reconstruction of vehicle-pedestrian collision are discussed: one knowing only the throw distance and the other when also impact to ground contact distance is known. The model is verified by field data available in the literature and by comportment with full scale numerical simulation. This paper has been withdrawn by the author due to error in spreadsheet program which results in misleading results in verification section of the article.
physics.class-ph↗
A Note on the Use of the Woodbury Formula To Solve Cyclic Block Tri-Diagonal and Cyclic Block Penta-diagonal Linear Systems of Equations
The article presents the theoretical background of the algorithms for solving cyclic block tridiagonal and cyclic block penta-diagonal systems of linear algebraic equations present in ref [1] and [2]. The theory is based on the Woodbury formula.
math-ph↗