scholarly journals Analysis of Friction, Spring and Wedging action

2021 ◽  
Author(s):  
Bo-Göran Wallner
Keyword(s):  
Equations Of Motion ◽  
Lagrangian Approach ◽  
Newtonian Mechanics ◽  
Spherical Object ◽  
Academic Paper

In this educational academic paper we will derive the equations of motion for a wedge in contact by friction with spherical object. This object is connected to a spring. We will approach the problem with Newtonian mechanics and compare this result with a Lagrangian approach and we will show that they with some restriction leads to the same result. The results from the equations of motion will be dicussed. The equations will then be numerically simulated for a number of different cases and the results will be analyzed.

scholarly journals Analysis of Friction, Spring and Wedging action

2021 ◽  
Author(s):  
Bo-Göran Wallner
Keyword(s):  
Equations Of Motion ◽  
Lagrangian Approach ◽  
Newtonian Mechanics ◽  
Spherical Object ◽  
Academic Paper

In this educational academic paper we will derive the equations of motion for a wedge in contact by friction with spherical object. This object is connected to a spring. We will approach the problem with Newtonian mechanics and compare this result with a Lagrangian approach and we will show that they with some restriction leads to the same result. The results from the equations of motion will be dicussed. The equations will then be numerically simulated for a number of different cases and the results will be analyzed.

scholarly journals Analysis of Friction, Spring and Wedging action

2021 ◽  
Author(s):  
Bo-Göran Wallner
Keyword(s):  
Equations Of Motion ◽  
Lagrangian Approach ◽  
Newtonian Mechanics ◽  
Spherical Object ◽  
Academic Paper

In this educational academic paper we will derive the equations of motion for a wedge in contact by friction with spherical object. This object is connected to a spring. We will approach the problem with Newtonian mechanics and compare this result with a Lagrangian approach and we will show that they with some restriction leads to the same result. The results from the equations of motion will be dicussed. The equations will then be numerically simulated for a number of different cases and the results will be analyzed.

Asynchronous seismic analysis of concrete-faced rockfill dams including dam–reservoir interaction

2005 ◽  
Vol 32 (5) ◽  
pp. 940-947 ◽  
Author(s):  
Alemdar Bayraktar ◽  
Kemal Haciefendioglu ◽  
Murat Muvafik
Keyword(s):  
Finite Element ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Coupled System ◽  
Lagrangian Approach ◽  
Element Formulation ◽  
Dam Reservoir ◽  
Torul Dam ◽  
Displacement Based ◽  
Isoparametric Finite Elements

Seismic response of concrete-faced rockfill (CFR) dams subjected to asynchronous base excitation is determined by considering dam–reservoir interaction. The equations of motion of the coupled system are obtained using the Lagrangian approach, and the surface sloshing motion is included in the finite element formulation. Torul dam constructed in the city, Gumushane, Turkey, is selected as a numerical example, and its material properties are considered in the analysis. The dam–reservoir interaction system is modelled using the Lagrangian (displacement-based) fluid and solid-quadrilateral-isoparametric finite elements. The east–west component of Erzincan earthquake, which occurred on 13 March 1992, recorded near the region of the dam is used as a ground motion. Propagation velocities of the seismic wave are chosen as 1000 m/s, 3000 m/s, and infinite. Stresses are calculated for empty and full reservoir cases and compared with each other.Key words: concrete-faced rockfill dam, Lagrangian approach, dam–reservoir interaction, finite element method, earthquake.

Stability of asymmetric rotors with asymmetric flexible disks

2021 ◽  
pp. 107754632110004
Author(s):  
Naim Khader
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Lagrangian Approach ◽  
Governing Equations ◽  
Stability Boundaries ◽  
System Solution ◽  
Asymmetric Rotor ◽  
Constant Coefficients ◽  
The Subject ◽  
Flexible Disk

The presented work examines the dynamic behavior of an asymmetric rotor with asymmetric flexible disk, contrary to previous works on the subject, where researchers examined the effect of either rigid disk asymmetry or disk flexibility at a time. Account for the asymmetry of flexible disk in rotors constitutes the new contribution in this work. The suggested mathematical model combines Lagrangian approach with Rayleigh–Ritz method to derive the governing equations of motion of the rotor. Account for asymmetry of the flexible disk results in complicated and lengthy expressions for the potential and kinetic energies of the rotor, required in the adopted Lagrangian approach. Using symbolic computation simplified the derivation of the governing equations of motion with constant coefficients in terms of rotating coordinate system. Solution of the resulting eigenvalue problem provided numerical results for rotors with symmetric and asymmetric flexible disks, required to assess the effect of disk flexibility and asymmetry on the resulting frequencies and stability boundaries of the examined rotor system.

scholarly journals Equations of motion of masses of the Chelomey pendulum model

2021 ◽  
Author(s):  
N. Kryshchuk ◽  
A. Tsybenko ◽  
Y. Lavrenko ◽  
A. Oleshchuk A.
Keyword(s):  
Software Package ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Newtonian Mechanics ◽  
Inertial Forces ◽  
Pendulum Model ◽  
Unit Work ◽  
Conservation Of Momentum ◽  
Mathcad Software ◽  
The Masses

Abstract. To verify the provisions stated by V.I. Bogomolov, B.I. Puzanov. and Linevich E.I. about the possibility of performing over-unit work by inertial forces, a closed mechanical system in the form of kinematically connected rotating masses is proposed for consideration. The research aimed, within the framework of Newtonian mechanics, to study the fulfillment of the laws of conservation of momentum, angular momentum and energy, to establish the possibility of performing work by inertial forces (centrifugal and Coriolis), to assess the change in kinetic parameters using the example of the Chelomey pendulum model. For the complex radial-circular motion of the masses of the Chelomey pendulum model, resolving equations are obtained. To verify the analytical calculations, algorithms for numerical solutions of the above problems have been developed and implemented in the MathCAD software package.

Particle Trajectories Around a Flying Slider

1998 ◽  
Vol 120 (1) ◽  
pp. 69-74 ◽  
Author(s):  
S. C. Lin ◽  
T. C. Kuo ◽  
C. C. Chieng
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Mean Free Path ◽  
Lagrangian Approach ◽  
Solid Surfaces ◽  
Flying Height ◽  
Sudden Expansion ◽  
Dominant Factor ◽  
Small Spacing

The Eulerian-Lagrangian approach is employed to simulate droplet trajectories due to the large-velocity gradient between two solid surfaces: a stationery block (slider) and a rotating plane (disk). Sudden expansion after the extremely small spacing will trap the particles in the open spaces. The fluid phase flowfield is obtained by solving Navier-Stokes equations with slip boundary correction in the Eulerian approach, and the droplet trajectories are calculated by integrating equations of motion with slip correction in the Lagrangian approach. Because of the extremely small spacing and the droplet size, Brownian motion effectively increases the probability of slider-head collisions, especially for extremely small particles. This study demonstrates that the effect due to particle size is the dominant factor in determining the probability of particle-slider collision, especially for particle sizes comparable with the air mean free path and the flowfield immediately adjacent to the solid surfaces. The results also show that lowering the flying height of the slider and increasing the disk velocity attracts the particles toward the gap between the disk and the slider.

A DERIVATION OF THE SCHWARZSCHILD EQUATIONS BY THE USE OF NEWTONIAN MECHANICS

1994 ◽  
Vol 09 (20) ◽  
pp. 3555-3569 ◽  
Author(s):  
D. SAVICKAS
Keyword(s):  
General Relativity ◽  
Euclidean Geometry ◽  
Equations Of Motion ◽  
Local Scale ◽  
Newtonian Potential ◽  
Newtonian Mechanics ◽  
Non Euclidean Geometry ◽  
Newton’S Laws ◽  
Particle Velocities ◽  
Exact Derivation

An exact derivation of both the Schwarzschild metric of general relativity and its equations of motion is made by the use of Newtonian mechanics. Although the form of Newtonian mechanics itself is not modified, the concepts of length and time on which it is based are modified in a manner that allows Newton’s laws to be expressed in a non-Euclidean space-time geometry. The lengths used in the laws are defined in terms of local-scale-measured distances, rather than the usual coordinate distances. Particle velocities are then defined in terms of these differential scale lengths. The Newtonian law of gravitation is also defined in terms of the gradient of the usual Newtonian potential with respect to these same scale lengths. It is shown that non-Euclidean geometry is imposed by the requirement that a photon in a gravitational field should maintain a constant total energy that is expressed in terms of its frequency, while also having a potential energy that is independent of the geometry of space. These conditions and modifications make it possible to derive equations of motion which are Newtonian, but which can also be reduced to forms that are identical to the Schwarzschild equations of motion for an orbiting particle or a gravitationally deflected photon.

A Newtonian mechanics formulation for the vibration of translating and rotating elastic continua

2019 ◽  
Vol 25 (10) ◽  
pp. 1639-1652 ◽  
Author(s):  
Robert L Lowe ◽  
Christopher G Cooley
Keyword(s):  
Control Volume ◽  
Broad Class ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Integral Form ◽  
Newtonian Mechanics ◽  
Elastic Continuum ◽  
Rotating Systems ◽  
Axially Moving ◽  
Kinematics And Kinetics

In this paper, we present a Newtonian mechanics formulation for modeling the vibration of a convecting elastic continuum, i.e., a system characterized by mean kinematic translation or rotation with small superposed vibrations. The proposed Newtonian approach complements customary energy-based techniques and serves as a convenient means to validate and physically interpret their results. We develop the equations of motion and matching conditions in a continuum mechanics setting with respect to a stationary inertial reference frame. Interaction of the convecting continuum with discrete space-fixed elements (e.g., springs and dampers) is enabled, without introducing time-dependent coefficients, through the use of Eulerian kinematics and kinetics. Kinematic discontinuities inherent in these interactions are accommodated by employing a global (or integral) form of balance of linear momentum applied to a space-fixed control volume. A generalized form of Navier's equation of elastic wave propagation is derived, with unsteady, Coriolis, centripetal, and convective contributions to the inertia. The resulting formulation is applied to a broad class of translating and rotating systems – including spinning rings, axially moving strings and beams, and general three-dimensional elastic structures – and shown to successfully reconcile with existing energy-based derivations in the literature.

General relativity exactly described in terms of Newton's laws within curved geometries

2014 ◽  
Vol 23 (08) ◽  
pp. 1430018 ◽  
Author(s):  
D. Savickas
Keyword(s):  
General Relativity ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Relativistic Equation ◽  
Equation Of Motion ◽  
Relativity Theory ◽  
Second Law ◽  
Newtonian Mechanics ◽  
Schwarzschild Solution ◽  
Conservation Of Energy

Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.

Closed and Expanded Form of Manipulator Dynamics Using Lagrangian Approach

1985 ◽  
Vol 107 (2) ◽  
pp. 223-225 ◽  
Author(s):  
T. Wang ◽  
D. Kohli
Keyword(s):  
Equations Of Motion ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
Lagrangian Approach ◽  
Alternative Derivation ◽  
Manipulator Dynamics ◽  
Lagrangian Equations ◽  
A Chain ◽  
Expanded Form ◽  
Simplified Form

An alternative derivation of the equations of motion of a chain of rigid bodies using Lagrangian equations of motion is presented. In an effort to reduce the complexity of the coefficients appearing in the equations of motion, a modified form of Lagrangian equations due to Silver [3] are utilized. This approach leads to a simplified form of coefficients of the equation of motion.

Sign in / Sign up

Export Citation Format

Share Document