The study of dynamics is based on Newton's law of motion; Newton's laws of motion are based on experiments. Dynamics is a part of Newtonian mechanics or classical mechanics, but since the 20th century, it is often understood as a branch of mechanics, focusing on the application of engineering technology.
A brief history of dynamics development
The development of mechanics, from expounding the simplest law of object balance to establishing the universal law of motion, has gone through about twenty centuries. A great deal of mechanical knowledge accumulated by predecessors played an important role in the later dynamics research, especially in the cosmology research of astronomers Copernicus and Kepler.
/kloc-At the beginning of the 7th century, Galileo, an Italian physicist and astronomer, revealed the principle of inertia of matter through experiments, and revealed the law of constant acceleration through the accelerated sliding experiment of an object on a smooth slope. He realized that the acceleration value of gravity near the ground does not change with the mass of the object, but is approximately constant, and then studied the universal laws of projectile motion and particle motion. Galileo's research initiated a research method widely used by later generations, starting with experiments and verifying theoretical results with experiments.
/kloc-In the 7th century, the calculus established by the great British scientist Newton and the German mathematician Leibniz brought the study of dynamics into a new era. Newton clearly put forward the law of inertia, the law of particle motion, the law of action and reaction, and the law of independent action of force in his masterpiece Mathematical Principles of Natural Philosophy published in 1687. He discovered the law of universal gravitation while searching for the causes of falling bodies and celestial bodies, and based on this, he deduced Kepler's law, verified the relationship between the centripetal acceleration of the moon's revolution around the earth and the acceleration of gravity, explained the tidal phenomenon on the earth, and established a very strict and perfect mechanical law system.
Focusing on Newton's second law, dynamics points out the relationship among force, acceleration and mass. Newton first introduced the concept of mass and distinguished it from the gravity of objects, indicating that the gravity of objects is only the gravity of the earth. After the laws of action and reaction were established, people began to study particle dynamics.
Newton's mechanical work and calculus work are inseparable. Since then, dynamics has become a rigorous science based on experiment, observation and mathematical analysis, thus laying the foundation of modern mechanics.
/kloc-huygens, a Dutch scientist in the 7th century, obtained the acceleration of the earth's gravity by observing the pendulum, and established the motion equation of the pendulum. Huygens established the concept of centrifugal force when studying conical pendulum; In addition, he also put forward the concept of moment of inertia.
After 100 Newton's law was published, Lagrange, a French mathematician, established a Lagrange equation that can be applied to a complete system. This set of equations is different from Newton's second law in the form of force and acceleration, but expressed by Lagrange function with generalized coordinates as independent variables. Lagrange system is more convenient to study some types of problems (such as small oscillation theory and rigid body dynamics) than Newton's law.
The concept of rigid body was put forward by Euler. 18th century Swiss scholar Euler extended Newton's second law to rigid bodies. He used three Euler angles to represent the angular displacement of a rigid body around a fixed point, defined the moment of inertia, and derived the differential equation of motion of a rigid body rotating at a fixed point. In this way, the general motion equation of a six-degree-of-freedom rigid body is established completely. For a rigid body, the sum of work done by internal forces is zero. Therefore, rigid body dynamics has become an approximate theory to study general solid motion.
1755, Euler established the dynamic equation of ideal fluid. The energy integral along the streamline (called Bernoulli equation) is obtained at 1758 Bernoulli. In 1822, Naville obtained the dynamic equation of incompressible fluid. 1855 Xu Hongniu studied shock waves in continuous media. In this way, dynamics has penetrated into the field of various forms of matter. For example, in elastic mechanics, due to the need to study collision, vibration, elastic wave propagation and other issues, elastic dynamics is established, which can be applied to the study of seismic wave propagation.
/kloc-Hamilton, a British mathematician in the 0 th and 9 th centuries, derived Hamilton's canonical equation by variational principle. The equation is a first-order system of equations with generalized coordinates and generalized momentum as variables and expressed by Hamiltonian function, and its form is symmetrical. The system that uses canonical equations to describe the formation of motion is called Hamiltonian system or Hamiltonian dynamics, which is the basis of classical statistical mechanics and an example of quantum mechanics. Hamiltonian system is suitable for perturbation theory, such as the perturbation problem of celestial mechanics, and plays an important role in understanding the general properties of motion of complex mechanical systems.
Lagrange dynamics and Hamiltonian dynamics are based on mechanical principles that are equivalent to Newton in classical mechanics, but their research approaches or methods are different. Mechanical systems that directly apply Newton's equations are sometimes called vector mechanics; The dynamics of Lagrange and Hamilton are called analytical mechanics.
Basic contents of dynamics
The basic contents of dynamics include particle dynamics, particle system dynamics, rigid body dynamics and D'Alembert principle. The applied disciplines developed on the basis of dynamics include celestial mechanics, vibration theory, motion stability theory, gyro mechanics, external ballistics, variable mass mechanics and the developing multi-rigid body system dynamics.
There are two basic problems in particle dynamics: one is to know the motion of a particle and find out the force acting on it; The second is to know the force acting on the particle and find the motion of the particle. When solving the first kind of problems, we only need to take the second derivative of the motion equation of the particle, and then we can get the acceleration of the particle, and then we can get the force by substituting it into Newton's second law. When solving the second kind of problems, it is necessary to solve the differential equation of particle motion or get the integral.
The general theorem of dynamics is the basic theorem of particle system dynamics, which includes momentum theorem, moment of momentum theorem, kinetic energy theorem and other theorems derived from these three basic theorems. Momentum, moment of momentum and kinetic energy are the basic physical quantities to describe the motion of particles, particle systems and rigid bodies. The relationship between the force or torque acting on the mechanical model and these physical quantities constitutes the general theorem of dynamics.
The characteristic of a rigid body is that the distance between its particles is constant. Euler dynamics equation is the basic equation of rigid body dynamics, and fixed-point rotation dynamics of rigid body is a classical theory in dynamics. The formation of gyro mechanics shows that the application of rigid body dynamics in engineering technology is of great significance. Multi-rigid-body system dynamics is a new branch formed by the development of new technology since 1960s, and its research method is different from the classical theory.
D'Alembert principle is a universal and effective method to study the dynamics of non-free particle systems. This method introduces the concept of inertia force on the basis of Newton's law of motion, so as to study the imbalance in dynamics by the method of studying equilibrium in statics, so it is also called dynamic and static method.
Application of dynamics
The study of dynamics enables people to master the laws of motion of objects and serve mankind better. For example, Newton discovered the law of gravity, explained Kepler's law, opened the way for modern interstellar navigation, and launched a spacecraft to inspect the moon, Mars, Venus and so on.
Since the advent of the theory of relativity in the early 20th century, the concepts of time and space in Newtonian mechanics and other basic concepts of mechanical quantities have changed greatly. The experimental results also show that classical dynamics is completely inapplicable when the speed of an object is close to the speed of light. However, in practical problems such as engineering, the speed of macroscopic objects is far less than the speed of light, so it is not only accurate enough to study with Newtonian mechanics, but also much simpler than relativistic calculation. Therefore, classical dynamics is still the basis for solving practical engineering problems.
In the mechanical system studied at present, there are more and more factors to be considered, such as variable mass, non-integral, nonlinear, non-conservative, feedback control, random factors and so on. , making the differential equations of motion more and more complicated, and fewer and fewer problems can be solved correctly. Many dynamic problems need to be solved approximately by numerical calculation. The application of micro, high-speed and large-capacity electronic computers has solved complex calculation problems.
At present, the research field of dynamic system is still expanding, such as adding heat and electricity to become system dynamics; Increase the activity of life system to become biodynamics and so on. , make the dynamics further develop in depth and breadth.