**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Statics

Summary

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather, is in static equilibrium with its environment. If \textbf F is the total of the forces acting on the system, m is the mass of the system and \textbf a is the acceleration of the system, Newton's second law states that \textbf F = m \textbf a , (the bold font indicates a vector quantity, i.e. one with both magnitude and direction). If \textbf a =0, then \textbf F = 0. As for a system in static equilibrium, the acceleration equals zero, the system is either at rest, or its center of mass moves at constant velocity.
The application of the assumption of zero acceleration to the summation of moments acting on the system leads to \textbf M = I \alpha = 0, where \textbf M is the summation of all moments

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related concepts (29)

Force

In physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pus

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. Phy

Galileo Galilei

Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei (ˌɡælᵻˈleɪoʊ_ˌɡælᵻˈleɪ , USalsoˌɡælᵻˈliːoʊ_- , ɡaliˈlɛːo ɡaliˈlɛi) or simply

Related courses (26)

Related publications (5)

ME-104: Introduction to structural mechanics

The student will acquire the basis for the analysis of static structures and deformation of simple structural elements. The focus is given to problem-solving skills in the context of engineering design.

ME-373: Finite element modelling and simulation

L'objectif de ce cours est d'apprendre à réaliser de manière rigoureuse et critique des analyses par éléments finis de problèmes concrets en mécanique des solides à l'aide d'un logiciel CAE moderne.

ME-372: Finite element method

L'étudiant acquiert une initiation théorique à la méthode des éléments finis qui constitue la technique la plus courante pour la résolution de problèmes elliptiques en mécanique. Il apprend à appliquer cette méthode à des cas simples et à l'exploiter pour résoudre les problèmes de la pratique.

Related people

No results

Related units

No results

Loading

Loading

Loading

Related lectures (67)

Sean Dennis Steven Gordon, Andreas Osterwalder, Silvia Tanteri, Junwen Zou

Stereodynamics experiments of Ne(3P2) reacting with Ar, Kr, Xe, and N2 leading to Penning and associative ionization have been performed in a crossed molecular beam apparatus. A curved magnetic hexapole was used to state-select and polarize Ne(3P2) atoms which were then oriented in a rotatable magnetic field and crossed with a beam of Ar, Kr, Xe, or N2. The ratio of associative to Penning ionization was recorded as a function of the magnetic field direction for collision energies between 320 cm−1 and 500 cm−1. Reactivities are obtained for individual states that differ only in Ω, the projection of the neon total angular momentum vector on the inter-particle axis. The results are rationalized on the basis of a model involving a long-range and a short-range reaction mechanism. Substantially lower probability for associative ionization was observed for N2, suggesting that predissociation plays a critical role in the overall reaction pathway.

2018The complex mechanisms involved in cellular processes have been increasingly understood this past century and the central role of the DNA molecule has been recognized. The base pair sequence along a DNA fragment is observed not only to encode the genomic information, but also to induce locally very specific physical properties, such as significantly bent or stiff regions. These variations in the molecule constitution are for instance believed to be involved in DNA-protein recognition and in nucleosomes positioning. Modelling the sequence dependent DNA mechanical properties is consequently an important step towards understanding many biological functions. However, in a cell, vastly different length scales are involved, ranging from a few base pairs to several thousands, which makes difficult the definition of \textit{one} appropriate model. A promising strategy seems then to be given by the multi-scale modeling of sequence dependent DNA mechanics. In this framework, the sequence dependent rigid base and rigid base pair models have been proposed. In these coarse grain models either each base pair or each base is described as a rigid body configuration, which leads to either a chain or a bichain representation of the DNA molecule. A sequence dependent configurational distribution has then been parametrized, either from experimental data or directly from atomistic molecular dynamic simulations, and provides an efficient and realistic description at the scale of hundreds of base pairs. Important questions that can be studied in these models are for instance the influence of the sequence on the probability of contact of two sites, which are distant along the molecule length, or on the expectation of the relative configuration of these two sites. In this thesis, we propose to approach these physical situations both from the discrete and the continuum modeling point of view, and then to discuss in which sense they actually constitute only one multi-scale point of view. In the first part, we discuss mechanical properties of heterogeneous rigid body chains and bichains, as well as continuum rod and birods, in classical statics and in equilibrium statistical physics. Equilibirum conditions, variational principles and configurational distributions are studied for single chains and rods, and then extended to bichains and birods. We have introduced in particular an original coordinate free Hamiltonian formulation in arc-length of the birod equilibrium conditions, and the notion of the persistence matrix for the configurational moment for chains and rods. We then present deterministic and stochastic exponential Cauchy-Born rules allowing to bridge the scales between the discrete and continuum representations. In the second part, we present applications of the proposed multi-scale mechanical theory for chains and rods to sequence dependent DNA modelling. We discuss the approximation using the birod model of most probable bichain configurations satisfying prescribed end conditions. Similarly, we then present the computation of the sequence dependent frame correlation matrix and the Flory persistence vector for chains using a continuum rod model. In addition, a homogenization method is proposed. These results are believed to constitute a substantial improvement in the multi-scale modeling of DNA mechanics.

Michele Ceriotti, Adrien Georges Nicolai, Riccardo Petraglia, Matthew Wodrich

Computational studies of organic systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chemical systems are dynamic entities where a multitude of molecular conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biological simulations, together with empirical force fields, and apply it to organic chemical problems. Replica-exchange molecular dynamics (REMD) permits thorough exploration of the potential energy surface. We combined REMD with density functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small molecular systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temperature-dependent rotational processes, and catalysis, we reveal new insights and chemistry that likely would be missed using static electronic structure computations. The REMD-DFTB methodology at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes.