He was the first to write analytical mechanics in the form of impulse component, which was called poisson bracket's operational symbol after use; His mechanics course has long been regarded as a standard textbook. In celestial mechanics, he extended Lagrange's and Laplace's research on the orbital stability of planets, and also calculated the gravitational force between spheres and ellipsoids. His formula for expressing gravity by the mass distribution inside the planet is still of practical value to the calculation of determining the shape of the earth through the orbit of artificial satellites in the 20th century. He independently obtained the integral of the fixed-point rotation differential equation of axisymmetric heavy rigid body, which is usually called Lagrange integrable case (working before Poisson, published after Poisson). In his paper "Research Report on the General Equation of Equilibrium and Motion of Elastic Solids and Fluids" published in 183 1, he was the first to give the physical properties of viscous fluids completely, that is, the constitutive relation. Before this, I Newton made a simple explanation in the book Mathematical Principles of Natural Philosophy (1687). A.-L Cauchy wrote the constitutive relation in component form (1823), but it lacked the static pressure term. Poisson solved many problems in heat conduction. He used trigonometric series, legendre polynomials and the expansion of Laplacian surface harmonic function, and many achievements about heat conduction were included in his monograph "Mathematical Theory of Heat". He solved many problems of electrostatics and magnetostatics; It laid the foundation of prejudice theory; The exterior ballistics and hydraulics are studied. A general integration method of elastic theoretical equations is proposed, and Poisson constant is introduced. He also solved the problem of elasticity theory by variational method. In Gravitation, he published a paper on the gravity of a sphere and its theoretical equations, and introduced the famous Poisson equation. His famous book Mechanics Course (2 volumes) developed the ideas of Lagrange and Laplace and became a widely used standard textbook. In celestial mechanics, he studied some problems about the theory of the moon and planets and the stability of the solar system, and calculated the universal gravitation caused by spheres and ellipsoids. 183 1 year, and he also published a new theory of capillary action.