Results 211 to 220 of about 1,590 (240)
Some of the next articles are maybe not open access.
Nature, 1968
Hamilton's Principle and Physical Systems By B. R. Gossick. Pp. xiii + 247. (New York: Academic Press, Inc.; London: Academic Press, Inc. (London), Ltd., 1967.) 68s.
openaire +1 more source
Hamilton's Principle and Physical Systems By B. R. Gossick. Pp. xiii + 247. (New York: Academic Press, Inc.; London: Academic Press, Inc. (London), Ltd., 1967.) 68s.
openaire +1 more source
1999
While it is in principle possible to solve any mechanical problem by integration of the equations d p/dt = F for each constituent of the system, in many cases this task can be quite complicated. The use of Cartesian coordinates can also be cumbersome, as can be taking into account the reaction forces of objects limiting the motion of the dynamical ...
Richard K. Cooper, Claudio Pellegrini
openaire +1 more source
While it is in principle possible to solve any mechanical problem by integration of the equations d p/dt = F for each constituent of the system, in many cases this task can be quite complicated. The use of Cartesian coordinates can also be cumbersome, as can be taking into account the reaction forces of objects limiting the motion of the dynamical ...
Richard K. Cooper, Claudio Pellegrini
openaire +1 more source
Hamilton's principle as substationarity principle
Acta Mechanica, 1984zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
1977
If a particle P r of mass m r moves with velocity ẋ r relative to an inertial reference frame, the quantity $${T^r = {\frac {1}{2}} m_r {\dot x^r} \cdot {\dot x^r} } = {{\frac {1}{2}} m_r ({\dot x^r})^2 }$$ (10.1.1) is called its kinetic energy.
openaire +1 more source
If a particle P r of mass m r moves with velocity ẋ r relative to an inertial reference frame, the quantity $${T^r = {\frac {1}{2}} m_r {\dot x^r} \cdot {\dot x^r} } = {{\frac {1}{2}} m_r ({\dot x^r})^2 }$$ (10.1.1) is called its kinetic energy.
openaire +1 more source
Gravitational motion and Hamilton’s principle
Il Nuovo Cimento, 1956I . In Newtonian mechanics a complete descript ion of any conserva t ive sys tem is conta ined in Hami l ton ' s principle: one func t ion in phase space, t he La~rangian, is enough for character iz ing the system. The e m p t y space equat ions of general i e l a t i v i t y are also der ived f rom a (four-dimensional) var ia t iona l pr inciple ...
openaire +1 more source
Hamilton's Principle as a Computational Device
American Journal of Physics, 1957Hamilton's principle is used as a computational device to obtain the period of a simple pendulum and a bead sliding along a parabolic wire to second-order terms in the amplitude. We assume a motion of the form θ = θ0 sinωt and ask the following question: How shall we choose the amplitude θ0 so as to make the line integral of the Lagrangian extremum for
openaire +1 more source
On the Reciprocal Form of Hamilton’s Principle
Journal of Applied Mechanics, 1973A complementary energy principle for dynamic analysis due to Toupin is critically examined. It is found that the variational principle is a necessary but not a sufficient condition for geometric compatibility and that consequently it allows the occurrence of spurious solutions.
openaire +2 more sources
1969
Consider a function f(x), a < x < b. Change the function at any (or every) point x = x 0 to f (x), while holding x = x 0 fixed. Form the difference $$\bar f\left( {{x_0}} \right) - f\left( {{x_0}} \right) \equiv \delta f$$ (6.1) which is called the variation of f.
openaire +1 more source
Consider a function f(x), a < x < b. Change the function at any (or every) point x = x 0 to f (x), while holding x = x 0 fixed. Form the difference $$\bar f\left( {{x_0}} \right) - f\left( {{x_0}} \right) \equiv \delta f$$ (6.1) which is called the variation of f.
openaire +1 more source
Hamilton’s Principle and Noether’s Theorem
2005Abstract This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses Noether’s theorem, a method for using symmetries of the extended Lagrangian to identify quantities that are conserved during the ...
openaire +1 more source
Hamilton’s principle as inequality for inelastic bodies
Continuum Mechanics and Thermodynamics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Q., Lv, Q. C., Liu, Y. R.
openaire +1 more source