tensors lagrangian equations of motion
Using the Lagrangian to obtain Equations of Motion pdf
Ngày tải lên :
28/06/2014, 06:20
... Zak presents an example of a cart with inverted pendulum Instead of using the Lagrangian equations of motion, he applies Newton’s law in its usual form There are a couple of differences between ... the equation of motion of a pendulum, so let’s try a more complicated example We hang the pendulum from a cart of mass M and position x, acted upon by a force u in the direction of x, and moving ... The Lagrangian equation of motion is thus m ¨ x cos θ + θ − g sin θ = ¨ (29) We can write this as a matrix differential equation M + m m cos θ cos θ x ¨ ¨ θ = ˙ m θ2 sin θ + u g sin θ (30) Of...
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Báo cáo " On equations of motion, boundary conditions and conserved energy-momentum of the rigid string " doc
Ngày tải lên :
05/03/2014, 14:20
... function q˙2 is unique because we have fixed the gauge The equations of motion (13) are equivalent to the following set of Hamilton equations of motion: ¯ H = −p1aq2a − p2aq2a − L q1 , q ′ , q”1, q2 ... of the rigid string model are not easy to carry out because equations of motion of the classical string and the corresponding canonical structure are rather complicated Hamilton description of ... boundary of the rectangle Ω The advantage of the form of the variation δS is that it involves the least possible number of derivatives of the variations δxµ The remaining derivatives of δx in...
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ON WEAK SOLUTIONS OF THE EQUATIONS OF MOTION OF A VISCOELASTIC MEDIUM WITH VARIABLE BOUNDARY V. G. pptx
Ngày tải lên :
23/06/2014, 00:20
... zero of a degree of a map implies the existence of solutions of the operator equation (6.1) and consequently the existence of a solution of (4.10) ((6.1) at λ = 1) Theorem 4.3 is proved Proof of ... and γn is the operator of taking of the normal component of a trace on the boundary of a function defined on Ω0 The operator γn 236 On weak solutions of the equations of motion 1/2 is bounded ... R(L) of the operator L is dense in E∗ We give the proof of this theorem in Section From Theorems 3.6 and 3.8 the next result follows 0,t (3.11) 222 On weak solutions of the equations of motion...
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Equations of motion in the state and confiruration spaces pptx
Ngày tải lên :
03/07/2014, 19:20
... State space A set of n second order differential equations is a set of order 2n that can be expressed in the form of a set of 2n first order equations 668 Appendix A EQUATIONS OF MOTION In a way ... number of degrees of freedom is large, it is expedient to resort to the methods of analytical mechanics One of the simplest approaches to writing the equations of motion of multidegrees of freedom ... B.2.2 Appendix B DYNAMICS OF MOTOR CYCLES Linearization of the equations of motion If the values of φ and v are small, it is possible to linearize the equations of motion As usual in linearized...
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Aircraft Flight Dynamics Robert F. Stengel Lecture8 Aircraft Equations of Motion 1
Ngày tải lên :
04/07/2014, 19:25
... # & # & " " mz %I " mz %B Rate of Change of Body-Referenced Angular Rate due to External Moment " • Next Time: Aircraft Equations of Motion – In the body frame of reference, the angular momentum ... −0.88 ×10 slug-ft Newton s 2nd Law, Applied to Rotational Motion " Rate of Change of Angular Momentum • In inertial frame, rate of change of angular momentum = applied moment (or torque), M" dh ... equal effect of angular rate on all particles of the aircraft" Inertia Matrix of an Aircraft with Mirror Symmetry " Ellipsoid of Inertia! Ixx x + Iyy y + Izz z = • Moments and Products of Inertia...
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Aircraft Flight Dynamics Robert F. Stengel Lecture9 Aircraft Equations of Motion 2
Ngày tải lên :
04/07/2014, 19:25
... ) e3 (t ) & & e4 (t ) % & Rigid-Body Equations of Motion Rigid-Body Equations of Motion " (Euler Angles) " Point-Mass Dynamics " • Inertial rate of change of translational position" • Translational ... Rate of change of Angular Position " φ = p + ( q sin φ + r cos φ ) tan θ θ = q cos φ − r sin φ ψ = ( q sin φ + r cos φ ) sec θ Rigid-Body Equations of Motion: Rate " • Rate of change of ... Rigid-Body Equations of Motion " (Attitude from Rotation Matrix) " • Translational Position " • rI = H v B • Supplemental Material Rate of change of Translational Position " Rate of change of Rotation...
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Introduction – Equations of motion G. Dimitriadis 08
Ngày tải lên :
05/08/2016, 01:00
... m M∞ # m m & Introduction to Aeroelasticity Equations of motion A Substituting the lift and moment expressions into the aeroelastic equations of motion gives: ! m S # # S Iα " $ ') &( &) %* ... disturbance equations They are valid for M∞>1.2 Introduction to Aeroelasticity Solution A The equations of motion are 2nd order linear ODEs and can be solved as usual A At each value of the Mach ... Aeroelasticity Pitch-Plunge airfoil A Flat plate airfoil with pitch and plunge degrees of freedom A Equations of motion: # m S & ) h, # K h % (* - + % $ S Iα ' +α $ Introduction to Aeroelasticity...
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Introduction – Equations of motion G. Dimitriadis 07
Ngày tải lên :
05/08/2016, 01:01
... Aeroelasticity Full equations of motion Introduction to Aeroelasticity Aerodynamic state equations of motion •! As in the 2D case, the unsteady equations of motion need to be completed by four extra equations ... •! The z-position of any point on the wing is ( ) z = y" + x # x f $ Introduction to Aeroelasticity Equations of motion •! As with the 2D pitch plunge wing, the equations of motion are derived ... y=0 and x=xf axes Introduction to Aeroelasticity 3D Quasi-steady equations of motion •! The full 3D quasi-steady equations of motion are given by •! They can be solved as usual Introduction to...
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Introduction – Equations of motion G. Dimitriadis 06
Ngày tải lên :
05/08/2016, 01:01
... used in flight flutter testing •! The quality of data, the number of transducers and the cost of the flight testing programme prohibited the use of more sophisticated methods •! These days, more ... measurement of particular modes of interest •! They are not used very much now They have several disadvantages: –! Single shot –! Difficult to fire two or more simultaneously –! Need thrusters of different ... characteristics of the aircraft at all •! On the other hand excitation levels can be low (we cannot ensure adequate levels of turbulence on test days) •! The signal-to-noise ratio of the response...
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Introduction – Equations of motion G. Dimitriadis 01
Ngày tải lên :
05/08/2016, 01:01
... the structural equations of motion: Introduction to Aeroelasticity Full aeroelastic equations of motion •! The equations of motion are second order, linear, ordinary differential equations •! Notice ... Aeroelasticity Equations of motion (1) •! The equations of motion can be obtained by inserting the expression for the total energy into Lagrange’s equation Introduction to Aeroelasticity Equations of motion ... degree -of freedom airfoil, quite capable of demonstrating most aeroelastic phenomena = pitch degree of freedom h= plunge degree of freedom xf= position of flexural axis (pivot) xc= position of centre...
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Introduction – Equations of motion G. Dimitriadis 05
Ngày tải lên :
05/08/2016, 01:01
... Complete Equations •! Equations (1) and (2) make up the complete aeroelastic system of equations •! Equations (1) are 2nd order Ordinary Differential Equations (ODEs) They describe the dynamics of ... Unsteady equations of motion This type of equation is known as integro-differential since it contains both integral and differential terms Introduction to Aeroelasticity Integro-differential equations ... known as the aerodynamic states They arise from the substitution of the approximate form of the Wagner function, !, in the equations of motion Introduction to Aeroelasticity Transform to ODEs (2)...
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Introduction – Equations of motion G. Dimitriadis 04
Ngày tải lên :
05/08/2016, 01:01
... that the equations of motion are only valid at zero airspeed or at the flutter condition •! They are also valid in the case of forced sinusoidal excitation •! We can calculate the response of an ... Aeroelasticity Basics (3) •! Therefore, the equations contain terms that depend on frequency •! The basis of the p-k method is to define •! Then, the equations of motion become $ & p M s + K s " #U Q( ... " n •! Where nl is the number of aerodynamic lags and "n are aerodynamic lag coefficients Introduction to Aeroelasticity Roger’s EOMs •! The equations of motion of the complete aeroelastic system...
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Introduction – Equations of motion G. Dimitriadis 03
Ngày tải lên :
05/08/2016, 01:01
... stream of speed U and zero angle of attack –! A pattern of sources of strength +2! on the top and surface of the flat plate, balanced by sources of strength -2! on the bottom surface –! A pattern of ... wing’s motion and then determine what the resulting value of V will be Introduction to Aeroelasticity Sinusoidal motion •! The most logical choice for prescribed motion is sinusoidal motion Slowly ... is defined by the wing’s motion Introduction to Aeroelasticity Wing motion •! Assume that the wing has pitch and plunge degrees of freedom •! The total upwash due to its motion is equal to ˙ (...
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Introduction – Equations of motion G. Dimitriadis 02
Ngày tải lên :
05/08/2016, 01:01
... full equations of motion can be readily solved analytically •! Define x=[h !]T •! Then assemble the equations of motion in the form •! Where M=A+!"b2B Introduction to Aeroelasticity Solution of Equations ... Equations •! Now the equations of motion are of first order, in the form •! Such equations can be solved by trying a solution of the form •! Where l are the eigenvalues of the system and can ... the flat plate of the previous example Introduction to Aeroelasticity Exercise •! Using the quasi-steady aeroelastic equations of motion and Matlab: –! Create a computer model of a 2D wing with...
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Aircraft Flight Dynamics Robert F. Stengel Lecture10 Linearized Equations and Modes of Motion
Ngày tải lên :
04/07/2014, 19:25
... Separation of the Equations of Motion into Longitudinal and LateralDirectional Sets Grumman F9F" Rigid-Body Equations of Motion (Scalar Notation) " Reorder the State Vector " State Vector" • • Rate of ... Longitudinal Modes of Motion " Lateral-Directional Modes of Motion in Steady, Level Flight " • Eigenvalues determine the damping and natural frequencies of the linear system s modes of motion" • Longitudinal ... lateral-directional motion" Effects of longitudinal controls on lateral-directional motion" Effects of lateral-directional controls on longitudinal motion" % Lon G Lat−Dir ' G Lat−Dir ' & Effects of lateral-directional...
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Animation the mechanics of motion
Ngày tải lên :
13/09/2012, 14:19
... animator and professional alike, not only in the form of texts such as this one, but an extensive range of animation of many types, live action video footage, an enormous archive of our cinematic ... work of Winsor McCay Those early animators gave us some of the most endearing and enduring examples of animation that few have equalled, even today Some of the work was simplistic, most of it ... playback/projection ϭ a slowing down of the action (slow motion action for analysis of wing beats of a humming bird) Timing Animation timing is the most basic and fundamental aspect of animation, yet it varies...
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Tài liệu Báo cáo khoa học: "DELIMITEDNESS AND TRAJECTORY-OF-MOTION EVENTS" pdf
Ngày tải lên :
22/02/2014, 10:20
... correlate of referential divisiveness, we assume that the set of individuals composed of a given kind is closed under the part -of relation; that is, whenever an individual y= is composed of a certain ... Trajectory -of- motion events are modeled as continuous constant rate changes of location in one dimension of the TRAJECTOR relative to one or more LANDMARKS (following Regier 1992 in his use of Langacker's ... domain of materials but also in the domain of eventualities, and derivatively in the domains of space and time as well This extension sets the stage for taking a sortal approach to the semantics of...
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Dynamic Vision for Perception and Control of Motion ppt
Ngày tải lên :
05/03/2014, 15:20
... Perception of Crossroads 297 10.1 General Introduction 297 10.1.1 Geometry of Crossings and Types of Vision Systems Required 298 10.1.2 Phases of Crossroad Perception and Turnoff ... resolution at the center of the retina is surrounded by receptive fields of increasing spread and a lower density of receptors per unit of area in the radial direction Vision of highly developed biological ... front, egomotion should be adjusted to this (improper) behavior of other traffic participants This shows that recognition of the intention of other subjects is important for a defensive style of driving...
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Đề tài " Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics " doc
Ngày tải lên :
06/03/2014, 08:21
... equally apply to the primitive equations subject to other kinds of boundary conditions As in the case of 3D Navier-Stokes equations the question of uniqueness of the weak solutions to this model ... caoc@fiu.edu Dept of Mathematics and Dept of Mechanical and Aerospace Engineering, University of California, Irvine, CA and Dept of Computer Science and Applied Mathematics, Weizmann Institute of Science, ... Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, A M S., Providence, R.I (1967) [20] J L Lions, R Temam, and S Wang, New formulations of the primitive equations of atmosphere and applications,...
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KODAK FILM HISTORY Chronology of Motion Picture Films - 1889 to 1939 doc
Ngày tải lên :
07/03/2014, 14:20
... development of a liquid-gate system for motion picture printers (joint award with PSC Technology, Inc and The Rickmark Camera Service Inc.) Motion Picture and Educational Markets Division renamed Motion ... to Eliminate need of formalin in stabilizer Process ECP-2B Awarded Scientific and Technical Award from the Academy of • Motion Picture Arts and Sciences for the development of EASTMAN Color High ... height and width dimension and not pitch 100 Years of Service to the Motion Picture Industry Awarded OSCAR Kodak celebrated the 100th anniversary of motion pictures by introducing Eastman EXR color...
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