Road vehicles -- Vehicle dynamics and road-holding ability -- Vocabulary

ISO 8855:2011 defines the principal terms used for road vehicle dynamics. The terms apply to passenger cars, buses and commercial vehicles with one or more steered axles, and to multi-unit vehicle combinations.

Véhicules routiers -- Dynamique des véhicules et tenue de route -- Vocabulaire

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Published
Publication Date
13-Dec-2011
Current Stage
6060 - International Standard published
Start Date
04-Nov-2011
Completion Date
14-Dec-2011
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INTERNATIONAL ISO
STANDARD 8855
Second edition
2011-12-15
Road vehicles — Vehicle dynamics and
road-holding ability — Vocabulary
Véhicules routiers — Dynamique des véhicules et tenue de route —
Vocabulaire
Reference number
ISO 8855:2011(E)
ISO 2011
---------------------- Page: 1 ----------------------
ISO 8855:2011(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2011

The reproduction of the terms and definitions contained in this International Standard is permitted in teaching manuals, instruction

booklets, technical publications and journals for strictly educational or implementation purposes. The conditions for such reproduction are:

that no modifications are made to the terms and definitions; that such reproduction is not permitted for dictionaries or similar publications

offered for sale; and that this International Standard is referenced as the source document.

With the sole exceptions noted above, no other part of this publication may be reproduced or utilized in any form or by any means,

electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or

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Published in Switzerland
ii © ISO 2011 – All rights reserved
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ISO 8855:2011(E)
Contents Page

Foreword ............................................................................................................................................................iv

Introduction.........................................................................................................................................................v

1 Scope............................................................................................................................................................1

2 Axis system.................................................................................................................................................1

3 Vehicle unit..................................................................................................................................................5

4 Vehicle geometry and masses...................................................................................................................6

5 Vehicle motion variables ............................................................................................................................8

5.1 Linear motion variables ..........................................................................................................................8

5.2 Angular motion variables .....................................................................................................................10

5.3 Terms relating to vehicle trajectory measures...................................................................................14

6 Forces and moments ................................................................................................................................15

6.1 Forces.....................................................................................................................................................15

6.2 Moments.................................................................................................................................................16

7 Suspension and steering geometry ........................................................................................................16

7.1 Steer and camber angles ......................................................................................................................16

7.2 Steering-axis geometry.........................................................................................................................20

8 Kinematics and compliances...................................................................................................................23

8.1 Kinematics..............................................................................................................................................23

8.2 Compliances..........................................................................................................................................25

9 Ride and roll stiffness...............................................................................................................................25

10 Tyres...........................................................................................................................................................26

10.1 Tyre geometry........................................................................................................................................26

10.2 Tyre forces and moments.....................................................................................................................27

10.3 Terms relating to tyre measures..........................................................................................................28

11 Input types and control modes................................................................................................................30

11.1 Input types..............................................................................................................................................30

11.2 Control modes .......................................................................................................................................30

12 Responses.................................................................................................................................................31

12.1 General response types........................................................................................................................31

12.2 Equilibrium and stability.......................................................................................................................31

12.3 Lateral response measures..................................................................................................................32

12.4 Understeer and oversteer measures ...................................................................................................33

Annex A (informative) Comments on terms and definitions ........................................................................37

Bibliography......................................................................................................................................................39

Alphabetical index............................................................................................................................................40

© ISO 2011 – All rights reserved iii
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ISO 8855:2011(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies

(ISO member bodies). The work of preparing International Standards is normally carried out through ISO

technical committees. Each member body interested in a subject for which a technical committee has been

established has the right to be represented on that committee. International organizations, governmental and

non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the

International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

ISO 8855 was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 9, Vehicle

dynamics and road-holding ability.

This second edition cancels and replaces the first edition (ISO 8855:1991), which has been technically

revised. It also incorporates the Addendum ISO 8855:1991/Add.1:1992.
iv © ISO 2011 – All rights reserved
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ISO 8855:2011(E)
Introduction

This International Standard defines terms appertaining to road vehicle dynamics, principally for use by design,

simulation and development engineers in the automotive industries. This second edition has been prepared in

response to a requirement to update the first, and to harmonize its contents with that of the comparable

standard published by SAE International (SAE J670:JAN2008). This revision extends the scope to include

provision for separate tyre and wheel axis systems, inclined and non-uniform road surfaces, tyre forces and

moments, multiple unit commercial vehicles, and two-axle vehicles possessed of four-wheel steer geometry.

The vocabulary contained in this International Standard has been developed from the previous edition, and

SAE J670, in order to facilitate accurate and unambiguous communication of the terms and definitions

employed in the test, analysis and general description of the lateral, longitudinal, vertical and rotational

dynamics of road vehicles.
© ISO 2011 – All rights reserved v
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INTERNATIONAL STANDARD ISO 8855:2011(E)
Road vehicles — Vehicle dynamics and road-holding ability —
Vocabulary
1 Scope

This International Standard defines the principal terms used for road vehicle dynamics. The terms apply to

passenger cars, buses and commercial vehicles with one or more steered axles, and to multi-unit vehicle

combinations.
2 Axis system
2.1
reference frame

geometric environment in which all points remain fixed with respect to each other at all times

2.2
inertial reference frame
Newtonian reference frame

reference frame (2.1) that is assumed to have zero linear and angular acceleration and zero angular velocity

NOTE In Newtonian physics, the Earth is assumed to be an inertial reference frame.

2.3
axis system
set of three orthogonal directions associated with X, Y and Z axes
GGG

NOTE A right-handed axis system is assumed throughout this International Standard, where: Z=×XY .

2.4
coordinate system

numbering convention used to assign a unique ordered trio (x, y, z) of values to each point in a reference

frame (2.1), and which consists of an axis system (2.3) plus an origin point
2.5
ground plane

horizontal plane in the inertial reference frame (2.2), normal to the gravitational vector

2.6
road surface

surface supporting the tyre and providing friction necessary to generate shear forces in the road plane (2.7)

NOTE The surface may be flat, curved, undulated or of other shape.
2.7
road plane
plane representing the road surface (2.6) within the tyre contact patch

NOTE 1 For an uneven road, a different road plane may exist at each tyre contact patch.

NOTE 2 For a planar road surface, the road plane is coincident with the road surface. For road surfaces with surface

contours having a wavelength similar to or less than the size of the tyre contact patch, as in the case of many ride events,

© ISO 2011 – All rights reserved 1
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ISO 8855:2011(E)

it is intended that an equivalent road plane be determined. Determination of the equivalent road plane is dependent on the

requirements of the analysis being performed. The equivalent road plane may not be coincident with the actual road

surface at the contact centre (4.1.4).
2.7.1
road plane elevation angle

angle from the normal projection of the X axis on to the ground plane (2.5) to the X axis

T T
2.7.2
road plane camber angle

angle from the normal projection of the Y axis on to the ground plane (2.5) to the Y axis

T T
2.8
earth-fixed axis system
(X , Y , Z )
E E E

axis system (2.3) fixed in the inertial reference frame (2.2), in which the X and Y axes are parallel to the

E E

ground plane (2.5), and the Z axis points upward and is aligned with the gravitational vector

NOTE The orientation of the X and Y axes is arbitrary and is intended to be based on the needs of the analysis or test.

E E
2.9
earth-fixed coordinate system
(x , y , z )
E E E

coordinate system (2.4) based on the earth-fixed axis system (2.8) with an origin that is fixed in the

ground plane (2.5)

NOTE The location of the origin is generally an arbitrary point defined by the user.

2.10
vehicle axis system
(X , Y , Z )
V V V

axis system (2.3) fixed in the reference frame (2.1) of the vehicle sprung mass (4.12), so that the X axis is

substantially horizontal and forwards (with the vehicle at rest), and is parallel to the vehicle's longitudinal plane

of symmetry, and the Y axis is perpendicular to the vehicle's longitudinal plane of symmetry and points to the

left with the Z axis pointing upward
See Figure 1.

NOTE 1 For multi-unit combinations a separate vehicle axis system may be defined for each vehicle unit (3.1)

(see Figure 2).

NOTE 2 The symbolic notation (X , Y , Z ), (X , Y , Z ), …, (X , Y , Z ) may be assigned to the vehicle

V,1 V,1 V,1 V,2 V,2 V,2 V,n V,n V,n
axis systems of a multi-unit combination with n vehicle units (3.1).
2.11
vehicle coordinate system
(x , y , z )
V V V

coordinate system (2.4) based on the vehicle axis system (2.10) with the origin located at the vehicle

reference point (2.12)
2.12
vehicle reference point
point fixed in the vehicle sprung mass (4.12)

NOTE The vehicle reference point may be defined in a variety of locations, based on the needs of the analysis or test.

Commonly used locations include the total vehicle centre of gravity, the sprung mass centre of gravity, the mid-wheelbase

(4.2) point at the height of the centre of gravity, and the centre of the front axle. For multi-unit combinations, a vehicle

reference point may be defined for each vehicle unit (3.1).
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ISO 8855:2011(E)
2.13
intermediate axis system
(X, Y, Z)

axis system (2.3) whose X and Y axes are parallel to the ground plane (2.5), with the X axis aligned with the

vertical projection of the X axis on to the ground plane (2.5)
See Figure 1.

NOTE 1 For multi-unit combinations, a separate intermediate axis system may be defined for each vehicle unit (3.1).

NOTE 2 The intermediate axis system is used to facilitate the definition of angular orientation terms and the

components of force, moment, and motion vectors. An intermediate coordinate system is not defined herein.

Key
1 vehicle reference point
2 ground plane
Figure 1 — Vehicle and intermediate axis systems
Figure 2 — Multi-unit axis systems
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ISO 8855:2011(E)
2.14
tyre axis system
(X , Y , Z )
T T T

axis system (2.3) whose X and Y axes are parallel to the local road plane (2.7), with the Z axis normal to

T T T

the local road plane, where the orientation of the X axis is defined by the intersection of the wheel plane

(4.1) and the road plane, and the positive Z axis points upward
NOTE A local tyre axis system may be defined at each wheel (see Figure 3).
2.15
tyre coordinate system
(x , y , z )
T T T

coordinate system (2.4) based on the tyre axis system (2.14) with the origin fixed at the contact centre

(4.1.4)
2.16
wheel axis system
(X , Y , Z )
W W W

axis system (2.3) whose X and Z axes are parallel to the wheel plane (4.1), whose Y axis is parallel to

W W W

the wheel-spin axis (4.1.1), and whose X axis is parallel to the local road plane (2.7), and where the

positive Z axis points upward
NOTE A local wheel axis system may be defined for each wheel (see Figure 3).
Key
1 wheel plane
2 road plane
3 wheel-spin axis
Figure 3 — Tyre and wheel axis system
2.17
wheel coordinate system
(x , y , z )
W W W

coordinate system (2.4) based on the wheel axis system (2.16) with the origin fixed at the wheel centre

(4.1.2)
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ISO 8855:2011(E)
2.18
cab axis system
(X , Y , Z )
C C C

axis system (2.3) fixed in the reference frame (2.1) of the cab sprung mass, so that the X axis is

substantially horizontal and forwards (with the vehicle at rest), and is parallel to the vehicle’s longitudinal plane

of symmetry, and where the Y axis is perpendicular to the cab’s longitudinal plane of symmetry and points to

the left with the Z axis pointing upward
NOTE A cab axis system applies only to vehicles with a suspended cab only.
2.19
cab coordinate system
(x , y , z )
C C C

coordinate system (2.4) based on the cab axis system (2.18) with the origin fixed at an arbitrary point

defined by the user
3 Vehicle unit
3.1
vehicle unit

rigid (i.e. non-articulating) vehicle element operating alone or in combination with one or more other rigid

elements joined at yaw-articulation joints

NOTE Tractor, semi trailer (3.2.2) and dolly (3.2.4) are examples of vehicle units. A drawbar trailer (3.2) may consist

of more than one vehicle unit.
3.2
trailer

vehicle unit (3.1) or combination of multiple vehicle units that is towed by another vehicle unit and can be

disconnected from its towing vehicle unit

NOTE A trailer may have a single axle or multiple axles positioned along its length.

3.2.1
full trailer

trailer (3.2) that has both front and rear running gear and, hence, provides fully its own vertical support

3.2.2
semi trailer

trailer (3.2) that has only rear running gear and hence depends on its towing vehicle unit (3.1) for a

substantial part of its vertical support

NOTE A semi trailer is typically coupled to the towing vehicle unit using a fifth-wheel coupling (3.2.6).

3.2.3
centre-axle trailer

trailer (3.2) with only rear running gear located only slightly aft of the nominal position of the centre of gravity

of the unit

NOTE A centre-axle trailer is typically coupled to the towing unit with a hitch coupling (3.2.7).

3.2.4
dolly

portion of a full trailer (3.2.1) that includes the steerable front running gear and tow bar

3.2.5
converter dolly

dolly (3.2.4) unit that couples to a semi trailer (3.2.2) with a fifth-wheel coupling (3.2.6) and thereby

“converts” the semi trailer to a full trailer (3.2.1)
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ISO 8855:2011(E)
3.2.6
fifth-wheel coupling

device used to connect a semi trailer (3.2.2) to its towing vehicle unit (3.1) that is designed to bear the very

substantial vertical load imposed by the front of the semi trailer

NOTE A fifth-wheel coupling provides rotational degrees of freedom in the Y and Z directions, but transmits moments

V V
about the X axis (all axes are in the towing vehicle unit).
3.2.7
hitch coupling

device used to connect a trailer (3.2) or converter dolly (3.2.5) tow bar to its towing vehicle unit (3.1), which

approximates a spherical joint by providing three rotational degrees of freedom within the normal operating

range

NOTE Typical examples of hitch couplings include ball hitches and pintle hitches.

4 Vehicle geometry and masses
4.1
wheel plane

plane normal to the wheel-spin axis (4.1.1), which is located halfway between the rim flanges

4.1.1
wheel-spin axis
axis of wheel rotation
NOTE This axis is coincident with the Y axis.
4.1.2
wheel centre
point at which the wheel-spin axis (4.1.1) intersects the wheel plane (4.1)
NOTE This point is the origin of the wheel coordinate system (2.17).
4.1.3
contact line
intersection of the wheel plane (4.1) and the road plane (2.7)
4.1.4
contact centre

intersection of the contact line (4.1.3) and the normal projection of the wheel-spin axis (4.1.1) on to the road

plane (2.7)

NOTE This point is the origin of the tyre coordinate system (2.15). The contact centre may not be the geometric centre

of the tyre contact patch (4.1.5) due to distortion of the tyre produced by external forces.

4.1.5
contact patch
footprint
portion of the tyre touching the road surface (2.6)
4.2
wheelbase

distance between the contact centres (4.1.4) on the same side of the vehicle, measured parallel to the X

axis, with the vehicle at rest on a horizontal surface, with zero steer angle (7.1.1)

NOTE 1 A vehicle may have a different wheelbase on the left and right sides by design. It is common practice to

average the left and right wheelbases; however, the difference may need to be taken into account in performing some

analyses. The wheelbase typically changes as the suspension trim height changes.
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ISO 8855:2011(E)

NOTE 2 This applies to two-axle vehicles only. ISO 21308-2:2006, 6.1, defines the “configuration wheelbase”, for

multi-axle vehicles, as the distance between the centre of the first front axle to the centre of the first driven rear axle. This

term is a dimensional description and is not used in dynamic analysis.
4.3
equivalent wheelbase

wheelbase (4.2) of a conventional two-axle vehicle (i.e. a vehicle with one steering front axle and one non-

steering rear axle) which, given similar front and rear cornering compliance properties, would exhibit the same

steady state (12.2.1) turning behaviour as is exhibited by the multi-axle vehicle

Key
1 turn centre
Figure 4 — Equivalent wheelbase
4.4
track

distance between the contact centres (4.1.4), on a single wheel axle, measured parallel to the Y axis, with

the vehicle at rest on a horizontal surface

NOTE For dual wheel axles, it is the distance between the points centrally located between the contact centres of the

inner and outer dual wheels.
4.5
articulation point

instant centre of rotation of two vehicle units (3.1) established by the mechanical coupling device joining

those two units, typically on the plane of symmetry of both units

NOTE 1 An articulation point may establish one, two, or three degrees of rotational freedom between the two coupled

units.

NOTE 2 For semi trailers (3.2.2), the longitudinal (X) coordinate of the articulation point is equal to the fifth-wheel

position (4.9). For full trailers (3.2.1), the longitudinal (X) coordinate of the articulation point is equal to the hitch

position (4.10). For vehicle combinations with more than one trailer (3.2), several articulation points may exist.

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ISO 8855:2011(E)
4.6
axle distance

average longitudinal distance between the contact centres (4.1.4), on two consecutive axles, measured

parallel to the X axis, with the vehicle at rest on a horizontal surface, at zero steer angle (7.1.1)

4.7
axle position

average longitudinal distance between the vehicle reference point (2.12) and the contact centres (4.1.4) of

the axle, measured parallel to the X axis, with the vehicle combination at rest on a horizontal surface at zero

steer angle (7.1.1)
4.8
trailer-axle position

average longitudinal distance between the contact centres (4.1.4) of the trailer (3.2) axle and the vertical

projection of the articulation point (4.5) (of the first trailer) on to the ground plane (2.5), with the vehicle

combination at rest on a horizontal surface in a straight-ahead condition
NOTE Trailers may consist of more than one axle and/or articulation points.
4.9
fifth-wheel position
kingpin position

average longitudinal distance between the contact centres (4.1.4) of the first driven rear axle of the towing

vehicle unit (3.1) and the projection of the articulation point (4.5) on to the ground plane (2.5), with the

vehicle combination at rest on a horizontal surface in a straight-ahead condition

NOTE Applicable to semi trailers (3.2.2) only.
4.10
hitch position

average longitudinal distance between the contact centres (4.1.4) of the first driven rear axle of the towing

vehicle unit (3.1) and the projection of the articulation point (4.5) on to the ground plane (2.5), with the

vehicle combination at rest on a horizontal surface in a straight-ahead condition

NOTE Applicable to full trailers (3.2.1) only.
4.11
unsprung mass

mass that is not carried by the suspension, but is supported directly by the tyres

4.12
sprung mass

mass that is supported by the suspension, i.e. the total vehicle mass less the unsprung mass (4.11)

NOTE It is common practice to allocate a portion of the mass of the suspension linkage, driveshafts and springs in the

sprung mass and the remainder in the unsprung mass.
5 Vehicle motion variables
5.1 Linear motion variables

For the definitions in this subclause, velocity and acceleration are relative to the earth-fixed axis system

(2.8) (X , Y , Z ). They are resolved into components in the intermediate axis system (2.13) (X, Y, Z).

E E E

NOTE It is also possible to resolve velocity and acceleration vectors into components in other axis systems (2.3). For

example, velocity and acceleration vectors may be resolved in the vehicle axis system (2.10) (X , Y , Z ) to produce v ,

V V V Xv
v , v and a , a , a .
Yv Zv Xv Yv Zv
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ISO 8855:2011(E)
5.1.1
vehicle velocity
vector quantity expressing the velocity of the vehicle reference point (2.12)
5.1.2
longitudinal velocity
component of the vehicle velocity (5.1.1) in the direction of the X axis
5.1.3
lateral velocity
component of the vehicle velocity (5.1.1) in the direction of the Y axis
5.1.4
vertical velocity
component of the vehicle velocity (5.1.1) in the direction of the Z axis
5.1.5
horizontal velocity
resultant of the longitudinal velocity (5.1.2) and the lateral velocity (5.1.3)
5.1.6
tyre trajectory velocity
vector quantity expressing the velocity of the contact centre (4.1.4)
5.1.7
tyre longitudinal velocity
component of the tyre trajectory velocity (5.1.6) in the X direction
5.1.8
tyre lateral velocity
component of the tyre trajectory velocity (5.1.6) in the Y direction
5.1.9
tyre vertical velocity
component of the tyre trajectory velocity (5.1.6) in the Z direction
5.1.10
vehicle acceleration

vector quantity expressing the acceleration of the vehicle reference point (2.12)

5.1.11
longitudinal acceleration
component of the vehicle acceleration (5.1.10) in the direction of the X axis
5.1.12
lateral acceleration
component of the vehicle acceleration (5.1.10) in the direction of the Y axis
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ISO 8855:2011(E)
5.1.13
vertical acceleration
component of the vehicle acceleration (5.1.10) in the direction of the Z axis
5.1.14
tangential acceleration

component of the vehicle acceleration (5.1.10) in the direction of the horizontal velocity (5.1.5)

5.1.15
centripetal acceleration

component of the vehicle acceleration (5.1.10) in the direction of the horizontal normal to the horizontal

velocity (5.1.5)
5.1.16
horizontal acceleration

resultant of the longitudinal acceleration (5.1.11) and the lateral acceleration (5.1.12), or the resultant of

the tangential acceleration (5.1.14) and the centripal acceleration (5.1.15)
5.2 Angular motion variables

For the definitions in this subclause, the sign of angles resulting from angular rotations is determined in

accordance with the right-hand rule and angular velocities and accelerations are relative to the earth-fixed

axis system (2.8) (X , Y , Z ); they are resolved into components in the intermediate axis system (2.13) (X,

E E E
Y, Z).

NOTE It is also possible to resolve angular velocity and acceleration vectors into components in other axis systems

(2.3). For example, angular velocity and acceleration vectors may be resolved in the vehicle axis system (2.10) (X , Y ,

V V
Z ) to produce ω , ω , ω and  
ωω,,ω .
V Xv Yv Zv XYVV ZV
5.2.1
yaw angle
angle from the X axis to the X axis, about the Z axis
E E
5.2.2
pitch angle
angle from the X axis to the X axis, about the Y axis

NOTE The pitch angle is not measured relative to the road surface (2.6), thus a vehicle at rest on an inclined road

surface has a non-zero pitch angle.
5.2.3
roll angle
angle from the Y axis to the Y axis, about the X axis
V V

NOTE These three angles; ψ, θ, ϕ are called the Vehicle Euler Angles. They define the orientation of the vehicle axis

system (2.10) (X , Y , Z ) with respect to the earth-fixed axis system (2.8) (X , Y , Z ), as a sequence of consecutive

V V V E E E
angular rotations as defined in Table 1.
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ISO 8855:2011(E)
Table 1 — Euler rotations
Angle produced
Rotation order Rotation nature
by rotation
X axis to the X axis
First rotation Yaw, ψ
about the Z axis
X axis to the X axis
Second rotation Pitch, θ
about the Y axis
Y axis to the Y axis
Third rotation Roll, ϕ
about the X axis
5.2.4
vehicle roll angle
angle from the Y axis to the Y axis, about the X axis
NOTE This angle is different from ro
...

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