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41 relations: Analytical mechanics, Arc length, Cambridge University Press, Canonical coordinates, Cartesian coordinate system, Configuration space (physics), Conserved quantity, Constraint (mathematics), Curvilinear coordinates, Cylindrical coordinate system, Degrees of freedom (mechanics), Degrees of freedom (physics and chemistry), Derivative, Dot product, Equations of motion, Euler–Lagrange equation, Generalized forces, Hamiltonian mechanics, Holonomic constraints, Homogeneous function, Imperial College Press, Kinetic energy, Lagrangian mechanics, Line element, Mass matrix, Multibody system, Orthogonal coordinates, Pendulum, Physical system, Point particle, Polar coordinate system, Position (vector), Real coordinate space, Rigid body dynamics, Spherical coordinate system, Spherical pendulum, Stiffness matrix, Time derivative, Total derivative, Tuple, Virtual work.
Analytical mechanics
In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics.
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Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Canonical coordinates
In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.
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Conserved quantity
In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables whose value remains constant along each trajectory of the system.
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Constraint (mathematics)
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.
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Curvilinear coordinates
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.
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Cylindrical coordinate system
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.
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Degrees of freedom (mechanics)
In physics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration.
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Degrees of freedom (physics and chemistry)
In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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Euler–Lagrange equation
In the calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation (although the latter name is ambiguous—see disambiguation page), is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary.
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Generalized forces
Generalized forces find use in Lagrangian mechanics, where they play a role conjugate to generalized coordinates.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Holonomic constraints
In classical mechanics a system may be defined as holonomic if all constraints of the system are holonomic.
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Homogeneous function
In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor.
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Imperial College Press
Imperial College Press (ICP) was formed in 1995 as a partnership between Imperial College of Science, Technology and Medicine in London and World Scientific publishing.
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Kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
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Lagrangian mechanics
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.
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Line element
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space.
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Mass matrix
In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative \dot q of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation where \dot q^\mathrm denotes the transpose of the vector \dot q. This equation is analogous to the formula for the kinetic energy of a particle with mass m and velocity v, namely and can be derived from it, by expressing the position of each particle of the system in terms of q. In general, the mass matrix M depends on the state q, and therefore varies with time.
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Multibody system
Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements.
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Orthogonal coordinates
In mathematics, orthogonal coordinates are defined as a set of d coordinates q.
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Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely.
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Physical system
In physics, a physical system is a portion of the physical universe chosen for analysis.
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Point particle
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Position (vector)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
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Real coordinate space
In mathematics, real coordinate space of dimensions, written R (also written with blackboard bold) is a coordinate space that allows several (''n'') real variables to be treated as a single variable.
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Rigid body dynamics
Rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.
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Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
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Spherical pendulum
In physics, a spherical pendulum is a higher dimensional analogue of the pendulum.
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Stiffness matrix
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation.
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Time derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function.
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Total derivative
In the mathematical field of differential calculus, a total derivative or full derivative of a function f of several variables, e.g., t, x, y, etc., with respect to an exogenous argument, e.g., t, is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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Virtual work
Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system.
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Redirects here:
Gaussian coordinates, Generalised velocities, Generalised velocity, Generalized Coordinate, Generalized coordinate, Generalized velocities, Generalized velocity.
References
[1] https://en.wikipedia.org/wiki/Generalized_coordinates
