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Diffstat (limited to 'ivp/spring.go')
| -rw-r--r-- | ivp/spring.go | 79 |
1 files changed, 79 insertions, 0 deletions
diff --git a/ivp/spring.go b/ivp/spring.go new file mode 100644 index 0000000..4c8798d --- /dev/null +++ b/ivp/spring.go @@ -0,0 +1,79 @@ +// Spring movement problem based on Hooke's law. +// +// Copyright (C) 2020 Juan Marín Noguera +// +// This file is part of Solvned. +// +// Solvned is free software: you can redistribute it and/or modify it under the +// terms of the GNU Lesser General Public License as published by the Free +// Software Foundation, either version 3 of the License, or (at your option) any +// later version. +// +// Solvned is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR +// A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more +// details. +// +// You should have received a copy of the GNU Lesser General Public License +// along with Solvned. If not, see <https://www.gnu.org/licenses/>. + +package ivp + +import ( + "math" + "github.com/JwanMan/mned" +) + +// A HookeSpring is a spring moving following Hooke's law. +// +// The spring is laid out horizontally over a table and has one end attached to +// a body which receives a certain friction from the table and such that the +// mass of the spring is negligible compared to the mass of the body. The other +// end of the spring is attached to a harmonic oscillator. The position of the +// body is measured as the (signed) distance to the rest position of the +// oscillator, and the velocity is measured in terms of such position. +// +// Only Mass and Spring are required, although the result of only specifying +// that would be really boring. Note also that, since we're following Hooke's +// law, the length of the spring can get negative. +type HookeSpring struct { + Mass float64 // Mass of the body (kg). + Spring float64 // Hooke's constant of the spring (kg/s^2). + X0 float64 // Initial position of the body (m). + V0 float64 // Initial velocity of the body (m/s). + Length float64 // Length of the spring at rest (m). + Friction float64 // Friction between the body and the table (kg/s). + Amplitude float64 // Amplitude of the oscillator's force (N). + AngleSpeed float64 // Angle speed of the oscillator (rad/s). +} + +// Get the IVP associated to the problem. The solution values have the form +// (length, speed), time starts at 0, and the harmonic oscillator starts at +// its natural position. +// +// The ODE is `m * x''(t) = A*sin(wt) - k*(x(t)-l) - rx'(t)`, where m is the +// mass of the body, x is its position, A is the amplitude of the oscillator, +// w is its angular velocity, k is the spring's constant, l is its length at +// rest, and r is the friction coefficient. +func (h *HookeSpring) ToIVP() mned.IVP { + adjSpring := h.Spring / h.Mass + adjFriction := h.Friction / h.Mass + adjAmplitude := h.Amplitude / h.Mass + w := h.AngleSpeed + length := h.Length + + return mned.IVP{ + Derivative: func(p mned.Point) ([]float64, bool) { + return []float64{ + p.Value[1], + adjAmplitude*math.Sin(w*p.Time) - + adjSpring*(p.Value[0]-length) - + adjFriction*p.Value[1], + }, true + }, + Start: mned.Point{ + Time: 0, + Value: []float64{h.X0, h.V0}, + }, + } +} |