The narrow strip is approximate to a rectangle, and the density of the rectangle is 1, so the center of mass is the center of mass, that is, the center of symmetry, which is the intersection of diagonal lines, so the ordinate (f+g)/2 and the abscissa x+dx/2.

It can be approximated as X. If it is not approximated, the higher-order infinitesimal of dx will appear in the later static moment calculation or be discarded.

When an object tends to rotate about a certain axis but does not rotate, the generated torque is static torque.

In geometric structure, centroid coordinates refer to the position of a point in a graph relative to each vertex. Take a triangle as an example, all points in the triangle can be represented by a matrix, and the matrix has a relationship with each vertex of the triangle.

The center of mass coordinate system is made up of Augustus Ferdinand m? It was put forward by Bius in 1827.

Extended data:

Law of conservation of centroid motion

(1) If ∑F e ≡0, ac = 0, vc = constant vector.

That is, when the main vector of the external force system is equal to zero, the acceleration of the center of mass is equal to zero, and the center of mass remains stationary or moves in a straight line at a constant speed.

Linear motion.

(2) If ∑Fxe ≡0, then acx = 0 and vcx = constant.

That is, when the algebraic sum of the projection of the external force system on an axis is equal to zero, the acceleration of the center of mass is projected to zero on this axis.

The center of mass remains stationary or moves at a constant speed along this axis.

These two cases are called conservation of centroid motion. The theorem of motion of the center of mass is often used to solve the constrained reaction.