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Instantiating a symbolic solution with specific numbers gives a numerical solution; for example, a = 0 gives (x, y) = (1, 0) (that is, x = 1, y = 0), and a = 1 gives (x, y) = (2, 1). The distinction between known variables and unknown variables is generally made in the statement of the problem, by phrases such as "an equation in x and y ", or ...
A configuration describes the pose of the robot, and the configuration space C is the set of all possible configurations. For example: If the robot is a single point (zero-sized) translating in a 2-dimensional plane (the workspace), C is a plane, and a configuration can be represented using two parameters (x, y).
Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
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In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem.It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.
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