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by Georges Vénizélos, Michel Borel
Movement Equations 3
Cover
Title
Copyright
Introduction
Table of Notations
1 Fundamental Principle of Dynamics
1.1. The fundamental principle of dynamics and its scalar consequences
1.2. Secondary principles
1.3. Motion of a set in a given frame λ
1.4. Motion of a non-deformable solid in a given frame
2 Solid in Space. Efforts and Links: Power
2.1. Degrees of freedom of a solid
2.2. Free solid
2.3. Linked solids and links
2.4. Virtual power developed on a material set
2.5. Power of the efforts exerted on a solid
2.6. Properties of power
3 Scalar Consequences and Movement Equations
3.1. Establishment principle of the movement equations
3.2. Movement equations of a solid
3.3. Movement equations of the free solid
3.4. Movement equations of the linked solid with configurable links
3.5. Energetic expression of the equations of analytical mechanics
3.6. Summary example
4 Particular Applications
4.1. Simulation of the motion of Earth
4.2. Foucault’s pendulum
5 Methodological Formulary
5.1. Reference outline on the motion of a solid
5.2. Kinematics of the solid
5.3. Principle of motion with fixed plane
5.4. Combination of motions
5.5. Kinetics of non-deformable solids
Bibliography
Index
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Other titles from iSTE in Mechanical Engineering and Solid Mechanics
Index
A, C
acceleration
Coriolis
drive
analytical mechanics
energetic equations
areal velocity
combination of accelerations
configurable links
energy-power equation
Lagrange equations
constant of areas
contact actions
Coriolis
acceleration
inertial torsor
F, I
Foucault
pendulum
hypocycloid
frame
a given
Galilean
closed
preferred
solar
terrestrial
free solid
dependent on time
dynamic torsor
fundamental principle of dynamics
holonomic links
independent of time
kinetic energy
kinetic torsor
movement equations
partial distributing torsors
scalar equations
vector equations
velocity distributing torsor
fundamental principle of dynamics
dynamic torsor
preferred time scale
inertial torsor drive
J, L
Jacobian
linked solid
configurable links
dynamic torsor
fundamental principle
kinetic energy
kinetic torsor
links
movement equations
partial distributing torsors
vector consequences
velocity distributing torsor
M, N
motion of a set in a given frame
effort generators
effort receivers
secondary principles
separation of effects
motion of Earth
motion of the pendulum
movement equations
choice of representative scalar consequences
establishment principle
torsor products
vector projection
non-deformable solid
Coriolis inertial torsor
drive inertial torsor
motion in a given frame
nonholonomic links
dependent on time
independent of time
O, P
orthoradial acceleration
parameter
independent
the situation of the solid
perfect configurable links
preferred time scale
power
of a continuous mechanical set
of a discrete force field
of a non-deformable mechanical set
of the efforts exerted on a solid
partial
properties
virtual
S, T
separation of effects
electromagnetic
gravitational
scalar equations
analytic mechanics
energy-power equation
Painlevé equation
theorem of dynamic moment
theorem of dynamic sum
via vector projection
solar system
Earth
ecliptic plane
rotation rate
trajectory of center of inertia
Sun
forces exerted upon Earth
solid
degrees of freedom
free
linked
solid with configurable links velocity distributing torsor
stationary motion
time-independent links
Lagrange equations
Painlevé equation
theorem of
dynamic moment
dynamic sum
virtual powers
virtual works
torsor
linear independence
U, V
universal gravitational constant
virtual velocities
solidifying
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