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1 results about "Characteristic equation" patented technology

In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-order differential equation or difference equation. The characteristic equation can only be formed when the differential or difference equation is linear and homogeneous, and has constant coefficients. Such a differential equation, with y as the dependent variable, superscript (n) denoting nᵗʰ-derivative, and aₙ, aₙ ₋ ₁, ..., a₁, a₀ as constants, aₙy⁽ⁿ⁾+aₙ₋₁y⁽ⁿ⁻¹⁾+⋯+a₁yʼ+a₀y=0, will have a characteristic equation of the form aₙrⁿ+aₙ₋₁rⁿ⁻¹+⋯+a₁r+a₀=0 whose solutions r₁, r₂, ..., rₙ are the roots from which the general solution can be formed.

Geometric profile parametric modeling method for protuberances of front fuselage of airplane

ActiveCN113704877AEfficient modelingEfficient aerodynamic shapeGeometric CADSustainable transportationClassical mechanicsEngineering
The invention belongs to the field of parametric modeling of airplanes, and particularly relates to a geometric profile parametric modeling method of a forefuselage protrusion of an airplane. The method comprises the following steps: constructing a front fuselage grid model; acquiring a front section and a rear section of the protrusion arrangement position on the front fuselage grid model along a predetermined direction; fitting a first sample line according to the geometrical shape of the geometrical projection of the front fuselage on the front fuselage profile, and obtaining the multipoint coordinates of the first sample line; fitting a second spline line according to the geometric shape of the geometric projection of the protrusion on the front fuselage section, and obtaining the multipoint coordinates of the second spline line; removing an inner point after the first spline line and the second spline line intersect to obtain a third spline line; and determining a front fuselage grid model with a protrusion according to the plurality of third spline lines. According to the method, the corresponding shape of the profile in a specific area can be directly controlled by controlling the characteristic equation and the corresponding size of the protrusion in the profile, so that the precise control of local geometry is realized.
Owner:SHENYANG AIRCRAFT DESIGN INST AVIATION IND CORP OF CHINA
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