Results 211 to 220 of about 466 (245)
Phong‐Rodrigues Extrinsic Vector‐Field Processing
Computer Graphics Forum, EarlyView.Abstract We introduce a new extrinsic discretization of tangent vector fields on triangle meshes that is continuous, with bounded derivatives that are continuous almost everywhere, supporting pointwise evaluation and integration of differential operators.
Hongyi Liu +4 more
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The Mathematical Gazette, 1935
Students find partial differential equations difficult not only on account of the inherent difficulties of the subject, but because of confusion, omissions, and, frequently, errors in the textbooks. To take an illustration, Piaggio (p. 147, new edition), begins with the statement that the equations
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Students find partial differential equations difficult not only on account of the inherent difficulties of the subject, but because of confusion, omissions, and, frequently, errors in the textbooks. To take an illustration, Piaggio (p. 147, new edition), begins with the statement that the equations
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1977
The fundamental equation in generalized coordinates has been found in (12.3.9) as $$\sum\limits_{s = 1}^n {\left( {\frac{d}{{dt}}\frac{{\partial T}}{{\partial \dot q_s }} - \frac{{\partial T}}{{\partial q_s }} - Q_s } \right)\delta q_s = 0,}$$ (13.1.1) where the kinetic energy T and the generalized forces Q s are, in general, functions of all
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The fundamental equation in generalized coordinates has been found in (12.3.9) as $$\sum\limits_{s = 1}^n {\left( {\frac{d}{{dt}}\frac{{\partial T}}{{\partial \dot q_s }} - \frac{{\partial T}}{{\partial q_s }} - Q_s } \right)\delta q_s = 0,}$$ (13.1.1) where the kinetic energy T and the generalized forces Q s are, in general, functions of all
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2010
Let \(\{\mathcal{M};d\mu \}\)be a material system whose mechanical state is described by N Lagrangian coordinates \(q = ({q}_{1},\ldots, {q}_{N})\). Since every point \(P \in \{\mathcal{M};d\mu \}\)is identified along its motion by the map (q, t) → P(q, t), the configuration of the system is determined, instant by instant, by the map \(t \rightarrow q ...
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Let \(\{\mathcal{M};d\mu \}\)be a material system whose mechanical state is described by N Lagrangian coordinates \(q = ({q}_{1},\ldots, {q}_{N})\). Since every point \(P \in \{\mathcal{M};d\mu \}\)is identified along its motion by the map (q, t) → P(q, t), the configuration of the system is determined, instant by instant, by the map \(t \rightarrow q ...
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The Solution of Lagrange's Equations by Analog Computation
IEEE Transactions on Electronic Computers, 1965A procedure for solving Lagrange's equations of motion by analog computation is discussed. The problem of summing loop instabilities is minimized because the coefficient matrix of the acceleration terms in the generalized force equations is positive definite.
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LAGRANGE Equations of Second Kind
1970The LAGRANGE-equation s of the 2nd kind are very well known. Therefore, only a special question will be illustrated by an example.
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2016
In this chapter Euler-Lagrange equations and the boundary conditions for a given Functional with only one independent variable with second order derivatives are derived. A general approach for solving one dimensional structures follows next. Euler-Lagrange equation leading to optimization is explained next by considering Brachistochrone problem.
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In this chapter Euler-Lagrange equations and the boundary conditions for a given Functional with only one independent variable with second order derivatives are derived. A general approach for solving one dimensional structures follows next. Euler-Lagrange equation leading to optimization is explained next by considering Brachistochrone problem.
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Lagrange’s differential equations
2002Differential equations of motion for the generalised coordinates can be obtained easily with the help of Lagrange’s central equation. The equations will be derived twice here. The first derivation will assume that the operations d and δ are not interchangeable, while the second one will assume that the operations are interchangeable. In the first case,
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1983
Jakob Bernoulli’s solution of 1696 to his brother Johann’s problem of the brachistochrone (§1.2) marked the introduction of variational considerations. However, it was not until the work of Euler (c. 1742) and Lagrange (1755) that the systematic theory now known as the calculus of variations emerged.
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Jakob Bernoulli’s solution of 1696 to his brother Johann’s problem of the brachistochrone (§1.2) marked the introduction of variational considerations. However, it was not until the work of Euler (c. 1742) and Lagrange (1755) that the systematic theory now known as the calculus of variations emerged.
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