Struct MassProperties

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pub struct MassProperties {
    pub mass_kg: f64,
    pub cg_m: DVec3,
    pub inertia_kg_m2: DMat3,
}

Expand description

Mass, center of mass and inertia tensor about the center of mass, in body axes.

Fields§

§mass_kg: f64

Mass, kg.

§cg_m: DVec3

Center of mass in body axes, m from the frame origin.

§inertia_kg_m2: DMat3

Inertia tensor about the center of mass, in body axes, kg·m².

Implementations§

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impl MassProperties

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pub const ZERO: Self

No mass, at the origin.

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pub fn point(mass_kg: f64, position_m: DVec3) -> Self

A point mass at position_m.

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pub fn axisymmetric( mass_kg: f64, cg_m: DVec3, axial_kg_m2: f64, transverse_kg_m2: f64, ) -> Self

A body symmetric about a line parallel to z through cg_m, with moment of inertia axial about that line and transverse about any perpendicular line through the center: the tensor diag(I_t, I_t, I_a).

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pub fn from_motor_element(element: &MassElement, nozzle_z_m: f64) -> Self

A motor-crate mass element on the body axis. The element’s axial coordinate runs toward the nose like z, so a nozzle exit at body z = nozzle_z_m puts the element’s center at nozzle_z_m + element.cg_m.

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pub fn inertia_about(&self, point_m: DVec3) -> DMat3

The inertia tensor about point_m instead of the center of mass (parallel-axis theorem).

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pub fn translated(&self, offset_m: DVec3) -> Self

The same body moved by offset_m.

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pub fn with_part_moved(&self, part: &MassProperties, offset_m: DVec3) -> Self

This body with one of its parts, part, moved by offset_m inside it: a ballast weight slid along the airframe, say. The mass is unchanged; with M the whole’s mass, m the part’s, c its center before the move and δ the offset,

cg' = cg + m δ / M
I'  = I_{cg'} + m [(|c + δ − cg'|² E − (c + δ − cg')(c + δ − cg')ᵀ) − (|c − cg'|² E − (c − cg')(c − cg')ᵀ)]

where I_{cg'} is this body’s inertia about the new center (parallel axis): the part’s point contribution about the new center is taken out where it was and put back where it is. Its own inertia about its center moves with it unchanged, so it cancels. part must be a part of this body; nothing checks that it is.

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pub fn without_part(&self, part: &MassProperties) -> Self

This body with one of its parts, part, taken out: a ballast weight or a payload released in flight. With M the whole’s mass and cg its center, m the part’s mass, c its center and I_p its own inertia about c,

M'  = M − m
cg' = (M cg − m c) / M'
I'  = I_{cg'} − (I_p + m (|c − cg'|² E − (c − cg')(c − cg')ᵀ))

where I_{cg'} is this body’s inertia about the new center (parallel axis), and the bracket is the part’s about it: Self::combine run backwards. part must be a part of this body, lighter than it; nothing checks that it is.

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pub fn rotated(&self, rotation: DQuat) -> Self

The same body turned by rotation about the frame origin: cg' = R cg, I' = R I Rᵀ.

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pub fn rolled(&self, angle_rad: f64) -> Self

The same body rolled by angle_rad about the body z axis (right-handed: x toward y).

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pub fn scaled(&self, factor: f64) -> Self

The same body with its mass scaled by factor and its shape unchanged: the inertia scales with the mass.

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pub fn copied(body: Self, offsets_m: &[[f64; 2]]) -> Self

Copies of body, one moved by each [x, y] of offsets_m across the axis, combined into one rigid body: a cluster’s tubes, or what each of them holds. One copy that is not moved is body itself, bit for bit; no offsets at all is no body (zero mass).

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pub fn placed(body: Self, places: &[Placement]) -> Self

Copies of body, one at each of places, combined into one rigid body: a cluster’s tubes or a pod set’s pods, or what each of them holds. Each copy is body rolled by its place’s angle about the body’s axis, then moved across it by its offset, so each carries its own parallel-axis term. One place that neither moves nor turns is body itself, bit for bit; no places at all is no body (zero mass).

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pub fn combine<'a>( parts: impl IntoIterator<Item = &'a MassProperties> + Clone, ) -> Self

The bodies combined into one rigid body.

With zero total mass the center is the plain average of the parts’ centers (the origin with no parts) and the tensors are summed, so massless placeholders stay finite.

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pub fn principal_moments_kg_m2(&self) -> [f64; 3]

The principal moments of inertia about the center of mass, ascending: the eigenvalues of the tensor.

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pub fn validate(&self) -> Result<(), DesignError>

Checks that this could be a real body: finite, non-negative mass; finite center; a symmetric tensor (to 1e-9 of its largest entry) whose principal moments are non-negative and obey the triangle inequality I_1 + I_2 ≥ I_3 (to the same tolerance), and that is zero when the mass is.