Lagrangian Dynamics ∗

نویسنده

  • Francesco Bullo
چکیده

The motion of a mechanical system is related via a set of dynamic equations to the forces and torques it is subject to. In this work we will be primarily interested in robots consisting of a collection of rigid links connected through joints that constrain the relative motion between the links. There are two main formalisms for deriving the dynamic equations for such mechanical systems: (1) Newton-Euler equations that are directly based on Newton’s laws, and (2) Euler-Lagrange equations that have their root in the classical work of d’Alembert and Lagrange on analytical mechanics and in the work of Euler and Hamilton on variational calculus. The main difference between the two approaches is in dealing with constraints. While Newton’s equations treat each rigid body separately and explicitly model the constraints through the forces required to enforce them, Lagrange and d’Alembert provided systematic procedures for eliminating the constraints from the dynamic equations, typically yielding a simpler system of equations. Constraints imposed by joints and by other mechanical components are one of the defining features of robots so that it is not surprising that the Lagrange’s formalism is often the method of choice in the robotics literature.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Effects of asymmetric stiffness on parametric instabilities of rotor

This work deals with effects of asymmetric stiffness on the dynamic behaviour of the rotor system. The analysis is presented through an extended Lagrangian Hamiltonian mechanics on the asymmetric rotor system, where symmetries are broken in terms of the rotor stiffness. The complete dynamics of asymmetries of rotor system is investigated with a case study. In this work, a mathematical model is ...

متن کامل

Computational fluid dynamics simulation of the flow patterns and performance of conventional and dual-cone gas-particle cyclones

One of the main concerns of researchers is the separation of suspended particles in a fluid. Accordingly, the current study numerically investigated the effects of a conical section on the flow pattern of a Stairmand cyclone by simulating single-cone and dual-cone cyclones. A turbulence model was used to analyze incompressible gas-particle flow in the cyclone models, and the Eulerian–Lagrangian...

متن کامل

Numerical Simulation of Scaling Effect on Bubble Dynamics in a Turbulent Flow around a Hydrofoil

A Lagrangian-Eulerian numerical scheme for the investigation of bubble motion in turbulent flow is developed. The flow is analyzed in the Eulerian reference frame while the bubble motion is simulated in the Lagrangian one. Finite volume scheme is used, and SIMPLEC algorithm is utilized for the pressure and velocity linkage. The Reynolds stresses are modeled by the RSTM model of Launder. Upwind ...

متن کامل

Dynamics of Space Free-Flying Robots with Flexible Appendages

A Space Free-Flying Robot (SFFR) includes an actuated base equipped with one or more manipulators to perform on-orbit missions. Distinct from fixed-based manipulators, the spacecraft (base) of a SFFR responds to dynamic reaction forces due to manipulator motions. In order to control such a system, it is essential to consider the dynamic coupling between the manipulators and the base. Explicit d...

متن کامل

Dynamics of Flexible Manipulators

This paper presents an application of Continuum (i.e. Lagrangian) and Finite Element Techniques to flexible manipulator arms for derivation of the corresponding Dynamic Equations of Motion. Specifically a one-link flexible arm is considered for detailed analysis, and the results are extended for the case of a two - link flexible manipulator. Numerical examples are given for the case of both one...

متن کامل

1 5 A ug 2 00 5 Lagrangian dynamics of the Navier - Stokes equation

Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid dynamics using the lagrangian. We attempt to develop a gauge invariant lagrangian which reconstructs the Navier-Stokes equation through the Euler-Lagrange eq...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004