panel set twindow_function akima_spline

The AKIMA_SPLINE function is very fast, since it uses local methods. It always produces good results for the value of the function being approximated. The AKIMA_SPLINE returns good estimates for the first derivative of the approximated function when the data points are evenly spaced. In instances where the data points are unevenly spaced, the estimate of the first derivative may be in error. In all cases, the second derivative of the function being approximated is unreliable.

To enter a function expression you enter a series of quoted strings.

The easiest way to enter a function expression in Adams View is to use the text editor in combination with the function builder. To invoke the text editor for entering a function expression, highlight the function field and then either pick the "EDIT" button at the top of the panel or type a ^t (control-t). The Adams View "function builder" is discussed below.

The syntactical correctness of a function expression can be investigated by using the "VERIFY" button at the upper right of the text editor. If there is a syntax error, a message is printed and the cursor is put near the problem. Proper unit consistency is not checked during function expression verification.

The remainder of this explanation will cover the components of FUNCTION expressions as summerized in the following table.

FUNCTION expressions can include integers, real numbers, and exponents. In other words, all numbers that are legal in Adams are legal in a FUNCTION expression.

In a FUNCTION expression, Adams allows any of the operators **, *, /, +, and -. Adams executes these operators according to the following precedence rules:

Adams subtracts TIME from one before it performs multiplication and division.

You can include the following system constants in a FUNCTION expression:

The following example of a FUNCTION with a system constant multiplies the system constant PI by the displacement of marker 10 with respect to marker 14:

A FUNCTION expression can contain any number of blank spaces. Five consecutive blank spaces in an expression do not terminate input of the expression (by indicating that what follows is a comment) as they do in an Adams statement. However, you should remember these two restrictions:

You can use a comma to continue FUNCTION expressions. You can break the expression anywhere except in the middle of a number, in the middle of a name, or between a function and its left bracket. Put a continuation comma in column one of the following line before the rest of the expression. If you break the expression at a comma that is part of the expression, you must use both the expression comma and the continuation comma. You may use more than one continuation comma to extend an expression over several lines.

The FUNCTIONS button at the right side of the Adams View text editor provides a means of constructing an Adams function string. These functions are briefly described below. Upon picking the FUNCTIONS button, you will be presented with the list of available functions in the "selection window". After you select the desired function, a panel will appear with fields representing the various parameters for the function. You will have full access to on-line help with this panel just like you have with regular panels. After you have completed the panel and selected the DONE button on the panel, the function string will be constructed and inserted at the current text cursor location in the text edit window.

A FUNCTION expression may access the current value of a system variable and use the value in computations. These values are accessed through a collection of functions. The accessible system variables include the following: Time, Mode, Displacements (Translational and Rotational), Velocities (Translational and Rotational), Accelerations (Translational and Rotational), Forces (Translational and Rotational), and User-defined variables. Invoke the text edit window and pick the FUNCTIONS button to get a list of functions that can be accessed.

In general, you use a function character string (such as DM, VX, or FZ) and a list of values (e.g. i1, i2, and i3) to access a system variable in an expression. For example, the value i1 may be the name of the marker for which you want to measure a quantity (such as displacement, velocity, acceleration, or force), i2 is the name of the marker with respect to which you want to measure the quantity, and i3 is the name of the marker you want to use to resolve the components of the quantity. If you do not specify marker i3, Adams computes the result in the ground reference frame.

Arithmetic IFs allow you to conditionally define FUNCTION. The format for arithmetic IFs is as follows:

Adams evaluates expression 1. If expression 1 is less than zero, the arithmetic IF equals expression 2; if expression 1 equals zero, the arithmetic IF equals expression 3; and if expression 1 is greater than zero, the arithmetic IF equals expression 4.

A FUNCTION expression with an arithmetic IF and its four expressions is as given below:

If the radial velocity between markers 10 and 31 is less than or equal to zero, the value of the FUNCTION expression is zero; but if the radial velocity between markers 10 and 31 is greater than zero, the value of the FUNCTION expression is six hundred.

In some ways, you may treat IF as a variable. For example, you can place it anywhere in the expression. In addition, you can nest arithmetic IFs nine levels deep.

You can use the FORTRAN functions ABS, ATAN, ATAN2, COS, EXP, LOG, LOG10, MIN, MAX, SIN, SQRT, and TAN in your expression. For more information about these functions, see a FORTRAN reference manual. Invoke the text edit window and pick the FUNCTIONS button to get a list of functions that can be accessed.

In general, an Adams function evaluates a mathematical equation and returns a value to your FUNCTION expression. The following table lists all the Adams functions and their purposes. Invoke the text edit window and pick the FUNCTIONS button to make a list of functions that can be accessed.

To enter a function expression you enter a series of quoted strings.

The easiest way to enter a function expression in Adams View is to use the text editor in combination with the function builder. To invoke the text editor for entering a function expression, highlight the function field and then either pick the "EDIT" button at the top of the panel or type a ^t (control-t). The Adams View "function builder" is discussed below.

The syntactical correctness of a function expression can be investigated by using the "VERIFY" button at the upper right of the text editor. If there is a syntax error, a message is printed and the cursor is put near the problem. Proper unit consistency is not checked during function expression verification.

The remainder of this explanation will cover the components of FUNCTION expressions as summerized in the following table.

FUNCTION expressions can include integers, real numbers, and exponents. In other words, all numbers that are legal in Adams are legal in a FUNCTION expression.

In a FUNCTION expression, Adams allows any of the operators **, *, /, +, and -. Adams executes these operators according to the following precedence rules:

Adams subtracts TIME from one before it performs multiplication and division.

You can include the following system constants in a FUNCTION expression:

The following example of a FUNCTION with a system constant multiplies the system constant PI by the displacement of marker 10 with respect to marker 14:

A FUNCTION expression can contain any number of blank spaces. Five consecutive blank spaces in an expression do not terminate input of the expression (by indicating that what follows is a comment) as they do in an Adams statement. However, you should remember these two restrictions:

You can use a comma to continue FUNCTION expressions. You can break the expression anywhere except in the middle of a number, in the middle of a name, or between a function and its left bracket. Put a continuation comma in column one of the following line before the rest of the expression. If you break the expression at a comma that is part of the expression, you must use both the expression comma and the continuation comma. You may use more than one continuation comma to extend an expression over several lines.

The FUNCTIONS button at the right side of the Adams View text editor provides a means of constructing an Adams function string. These functions are briefly described below. Upon picking the FUNCTIONS button, you will be presented with the list of available functions in the "selection window". After you select the desired function, a panel will appear with fields representing the various parameters for the function. You will have full access to on-line help with this panel just like you have with regular panels. After you have completed the panel and selected the DONE button on the panel, the function string will be constructed and inserted at the current text cursor location in the text edit window.

A FUNCTION expression may access the current value of a system variable and use the value in computations. These values are accessed through a collection of functions. The accessible system variables include the following: Time, Mode, Displacements (Translational and Rotational), Velocities (Translational and Rotational), Accelerations (Translational and Rotational), Forces (Translational and Rotational), and User-defined variables. Invoke the text edit window and pick the FUNCTIONS button to get a list of functions that can be accessed.

In general, you use a function character string (such as DM, VX, or FZ) and a list of values (e.g. i1, i2, and i3) to access a system variable in an expression. For example, the value i1 may be the name of the marker for which you want to measure a quantity (such as displacement, velocity, acceleration, or force), i2 is the name of the marker with respect to which you want to measure the quantity, and i3 is the name of the marker you want to use to resolve the components of the quantity. If you do not specify marker i3, Adams computes the result in the ground reference frame.

Arithmetic IFs allow you to conditionally define FUNCTION. The format for arithmetic IFs is as follows:

Adams evaluates expression 1. If expression 1 is less than zero, the arithmetic IF equals expression 2; if expression 1 equals zero, the arithmetic IF equals expression 3; and if expression 1 is greater than zero, the arithmetic IF equals expression 4.

A FUNCTION expression with an arithmetic IF and its four expressions is as given below:

If the radial velocity between markers 10 and 31 is less than or equal to zero, the value of the FUNCTION expression is zero; but if the radial velocity between markers 10 and 31 is greater than zero, the value of the FUNCTION expression is six hundred.

In some ways, you may treat IF as a variable. For example, you can place it anywhere in the expression. In addition, you can nest arithmetic IFs nine levels deep.

You can use the FORTRAN functions ABS, ATAN, ATAN2, COS, EXP, LOG, LOG10, MIN, MAX, SIN, SQRT, and TAN in your expression. For more information about these functions, see a FORTRAN reference manual. Invoke the text edit window and pick the FUNCTIONS button to get a list of functions that can be accessed.

In general, an Adams function evaluates a mathematical equation and returns a value to your FUNCTION expression. The following table lists all the Adams functions and their purposes. Invoke the text edit window and pick the FUNCTIONS button to make a list of functions that can be accessed.

If a spline is available by default, you may identify it by entering its name only. If it is not, you must enter its full name. To identify a spline under another model, for instance, you may need to enter the model name as well. For example, you may specify spline 'stiffness' from model 'suspension' by entering ".suspension.stiffness". If you type a "?", Adams View will list the splines available by default.